##############ECHO OF PROBLEM################# ##############R:Temp/arctan_sqrtpostode.ode################# diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-1.0) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb $glob_max_h=c(0.01) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-2.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=12 $glob_max_minutes=(3.0) $glob_subiter_method=2 $glob_max_iter=1000000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) $glob_h_reason=1 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) + c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) 0.20677340069798467 y[1] (numeric) 0.20677340069798467 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (closed_form) 0.20984334727926424 y[1] (numeric) 0.209843347300974 absolute error 2.1709772868305777e-11 relative error 1.0345704617175175e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 1.01 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (closed_form) 0.2129275836241571 y[1] (numeric) 0.2129275836674298 absolute error 4.3272718741604876e-11 relative error 2.0322739780857352e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 1.02 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (closed_form) 0.2160260266070555 y[1] (numeric) 0.2160260266717479 absolute error 6.46923903335761e-11 relative error 2.99465723411418e-08% Desired digits 12 Estimated correct digits 13 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 1.03 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (closed_form) 0.21913859427641658 y[1] (numeric) 0.2191385943623858 absolute error 8.59692317334293e-11 relative error 3.9230529892415756e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.04 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (closed_form) 0.22226520582692944 y[1] (numeric) 0.22226520593403468 absolute error 1.0710524134260879e-10 relative error 4.818803777412111e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.05 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (closed_form) 0.22540578157261004 y[1] (numeric) 0.22540578170071351 absolute error 1.281034722744323e-10 relative error 5.6832380864714546e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.06 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (closed_form) 0.22856024292078425 y[1] (numeric) 0.22856024306974865 absolute error 1.489643963736853e-10 relative error 6.517511290242821e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.07 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (closed_form) 0.23172851234690883 y[1] (numeric) 0.23172851251659946 absolute error 1.6969062266447565e-10 relative error 7.322820180644863e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.08 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (closed_form) 0.23491051337021185 y[1] (numeric) 0.2349105135604963 absolute error 1.9028445485957945e-10 relative error 8.10029539034283e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.09 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999999999999999 y[1] (closed_form) 0.23810617053010974 y[1] (numeric) 0.23810617074085644 absolute error 2.1074669787068956e-10 relative error 8.850954908119005e-08% Desired digits 12 Estimated correct digits 13 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8899999999999999 y[1] (closed_form) 0.24131540936336782 y[1] (numeric) 0.24131540959444656 absolute error 2.3107873947658675e-10 relative error 9.575797090049608e-08% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.11 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (closed_form) 0.24453815638197796 y[1] (numeric) 0.24453815663326173 absolute error 2.512837715684668e-10 relative error 1.0275851232637575e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.12 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8699999999999999 y[1] (closed_form) 0.24777433905172952 y[1] (numeric) 0.24777433932309176 absolute error 2.713622382355396e-10 relative error 1.0951991205953152e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1300000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8599999999999999 y[1] (closed_form) 0.25102388577143087 y[1] (numeric) 0.2510238860627478 absolute error 2.913169150353667e-10 relative error 1.1605147220955083e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1400000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (closed_form) 0.25428672585277523 y[1] (numeric) 0.2542867261639232 absolute error 3.111479962569774e-10 relative error 1.223610848004403e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1500000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8399999999999999 y[1] (closed_form) 0.2575627895008057 y[1] (numeric) 0.2575627898316639 absolute error 3.308582297023577e-10 relative error 1.284573095141613e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1600000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8299999999999998 y[1] (closed_form) 0.26085200779497697 y[1] (numeric) 0.26085200814542414 absolute error 3.5044717128229763e-10 relative error 1.3434712435019485e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1700000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (closed_form) 0.26415431267076794 y[1] (numeric) 0.26415431304068654 absolute error 3.69918595755081e-10 relative error 1.4003882503941313e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1800000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8099999999999998 y[1] (closed_form) 0.2674696369018501 y[1] (numeric) 0.2674696372911227 absolute error 3.892726141430103e-10 relative error 1.4553899225797232e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.1900000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7999999999999998 y[1] (closed_form) 0.27079791408276455 y[1] (numeric) 0.27079791449127677 absolute error 4.0851222404825194e-10 relative error 1.5085501135854298e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2000000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (closed_form) 0.2741390786121132 y[1] (numeric) 0.27413907903974954 absolute error 4.2763637075893257e-10 relative error 1.5599248852952003e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2100000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7799999999999998 y[1] (closed_form) 0.2774930656762198 y[1] (numeric) 0.27749306612286706 absolute error 4.4664727472110144e-10 relative error 1.609579949800445e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2200000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7699999999999998 y[1] (closed_form) 0.28085981123326675 y[1] (numeric) 0.280859811698814 absolute error 4.6554726740311025e-10 relative error 1.6575787947690822e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2300000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (closed_form) 0.2842392519978785 y[1] (numeric) 0.28423925248221577 absolute error 4.843372924945299e-10 relative error 1.703977508701525e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2400000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7499999999999998 y[1] (closed_form) 0.2876313254261347 y[1] (numeric) 0.28763132592915297 absolute error 5.030182936849315e-10 relative error 1.7488300098735573e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2500000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7399999999999998 y[1] (closed_form) 0.2910359697010003 y[1] (numeric) 0.2910359702225926 absolute error 5.215922693757591e-10 relative error 1.792191768981765e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2600000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (closed_form) 0.29445312371816224 y[1] (numeric) 0.29445312425822123 absolute error 5.400589975224079e-10 relative error 1.8341085694826215e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2700000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7199999999999998 y[1] (closed_form) 0.2978827270722455 y[1] (numeric) 0.297882727630666 absolute error 5.584204765263223e-10 relative error 1.8746319466549283e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2800000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7099999999999997 y[1] (closed_form) 0.3013247200434108 y[1] (numeric) 0.30132472062008936 absolute error 5.766785382554929e-10 relative error 1.91381091525585e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.2900000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6999999999999997 y[1] (closed_form) 0.30477904358431207 y[1] (numeric) 0.3047790441791454 absolute error 5.948333492433733e-10 relative error 1.9516871706398098e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3000000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6899999999999997 y[1] (closed_form) 0.308245639307398 y[1] (numeric) 0.3082456399202844 absolute error 6.128864082910468e-10 relative error 1.988305202526631e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3100000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6799999999999997 y[1] (closed_form) 0.3117244494725542 y[1] (numeric) 0.3117244501033942 absolute error 6.308400468668651e-10 relative error 2.023710517202814e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3200000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6699999999999997 y[1] (closed_form) 0.3152154169750747 y[1] (numeric) 0.3152154176237673 absolute error 6.486925996362913e-10 relative error 2.057934240213847e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3300000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6599999999999997 y[1] (closed_form) 0.318718485333934 y[1] (numeric) 0.31871848600038133 absolute error 6.664473417572481e-10 relative error 2.0910219282040853e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3400000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6499999999999997 y[1] (closed_form) 0.32223359868037926 y[1] (numeric) 0.32223359936448415 absolute error 6.841048838523989e-10 relative error 2.123009166809314e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3500000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6399999999999997 y[1] (closed_form) 0.3257607017468058 y[1] (numeric) 0.3257607024484722 absolute error 7.016663916559196e-10 relative error 2.15393197489267e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3600000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6299999999999997 y[1] (closed_form) 0.32929973985592076 y[1] (numeric) 0.3292997405750525 absolute error 7.191317541455078e-10 relative error 2.1838212033211782e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3700000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6199999999999997 y[1] (closed_form) 0.3328506589101763 y[1] (numeric) 0.3328506596466804 absolute error 7.365041354567836e-10 relative error 2.2127164713095493e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3800000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6099999999999997 y[1] (closed_form) 0.33641340538147935 y[1] (numeric) 0.33641340613526166 absolute error 7.5378231434442e-10 relative error 2.2406429181668933e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.3900000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5999999999999996 y[1] (closed_form) 0.3399879263011445 y[1] (numeric) 0.339987927072113 absolute error 7.709685112544662e-10 relative error 2.2676349705771032e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4000000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5899999999999996 y[1] (closed_form) 0.34357416925010664 y[1] (numeric) 0.3435741700381706 absolute error 7.880639474322493e-10 relative error 2.2937229220470703e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4100000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5799999999999996 y[1] (closed_form) 0.3471720823493718 y[1] (numeric) 0.34717208315444037 absolute error 8.05068567366618e-10 relative error 2.3189323344163615e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4200000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5699999999999996 y[1] (closed_form) 0.3507816142506983 y[1] (numeric) 0.35078161507268113 absolute error 8.219828151467823e-10 relative error 2.3432893337429126e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4300000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5599999999999996 y[1] (closed_form) 0.3544027141275037 y[1] (numeric) 0.354402714966314 absolute error 8.388102989975721e-10 relative error 2.366828090080012e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4400000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5499999999999996 y[1] (closed_form) 0.3580353316660023 y[1] (numeric) 0.3580353325215508 absolute error 8.555484654060308e-10 relative error 2.389564352280572e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4500000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5399999999999996 y[1] (closed_form) 0.36167941705653384 y[1] (numeric) 0.36167941792873537 absolute error 8.72201533219652e-10 relative error 2.41153212510105e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4600000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5299999999999996 y[1] (closed_form) 0.3653349209851209 y[1] (numeric) 0.3653349218738892 absolute error 8.887683367042598e-10 relative error 2.4327494735726535e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4700000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5199999999999996 y[1] (closed_form) 0.36900179462520954 y[1] (numeric) 0.3690017955304582 absolute error 9.052486538152493e-10 relative error 2.4532364530495004e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4800000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5099999999999996 y[1] (closed_form) 0.372679989629606 y[1] (numeric) 0.3726799905512518 absolute error 9.216457597105432e-10 relative error 2.4730218561681716e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.4900000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.49999999999999956 y[1] (closed_form) 0.37636945812261 y[1] (numeric) 0.3763694590605698 absolute error 9.379597654124439e-10 relative error 2.4921250786159284e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5000000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.48999999999999955 y[1] (closed_form) 0.3800701526923205 y[1] (numeric) 0.3800701536465117 absolute error 9.541912260324636e-10 relative error 2.5105660606948883e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5100000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.47999999999999954 y[1] (closed_form) 0.383782026383122 y[1] (numeric) 0.3837820273534625 absolute error 9.703405301486612e-10 relative error 2.528363663336306e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5200000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.46999999999999953 y[1] (closed_form) 0.38750503268834 y[1] (numeric) 0.3875050336747494 absolute error 9.864093986067246e-10 relative error 2.545539581159627e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5300000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4599999999999995 y[1] (closed_form) 0.39123912554306806 y[1] (numeric) 0.39123912654546567 absolute error 1.002397609362049e-09 relative error 2.5621098298148196e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5400000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4499999999999995 y[1] (closed_form) 0.3949842593171482 y[1] (numeric) 0.39498426033545514 absolute error 1.0183069387714738e-09 relative error 2.5780949867013195e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5500000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4399999999999995 y[1] (closed_form) 0.39874038880831764 y[1] (numeric) 0.3987403898424546 absolute error 1.0341369427457892e-09 relative error 2.593509390499489e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5600000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4299999999999995 y[1] (closed_form) 0.40250746923549885 y[1] (numeric) 0.4025074702853875 absolute error 1.0498886759968684e-09 relative error 2.608370666986555e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5700000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4199999999999995 y[1] (closed_form) 0.4062854562322431 y[1] (numeric) 0.4062854572978068 absolute error 1.065563692836946e-09 relative error 2.6226971123176086e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5800000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4099999999999995 y[1] (closed_form) 0.41007430584031823 y[1] (numeric) 0.41007430692148056 absolute error 1.0811623263329295e-09 relative error 2.636503460311729e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.5900000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.39999999999999947 y[1] (closed_form) 0.4138739745034328 y[1] (numeric) 0.4138739756001179 absolute error 1.096685131596331e-09 relative error 2.6498045278448277e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6000000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.38999999999999946 y[1] (closed_form) 0.41768441906109866 y[1] (numeric) 0.4176844201732308 absolute error 1.112132164138302e-09 relative error 2.662613478947176e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6100000000000005 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.37999999999999945 y[1] (closed_form) 0.42150559674262134 y[1] (numeric) 0.42150559787012754 absolute error 1.1275061995164037e-09 relative error 2.6749495338371004e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6200000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.36999999999999944 y[1] (closed_form) 0.4253374651612303 y[1] (numeric) 0.4253374663040353 absolute error 1.1428050172845872e-09 relative error 2.686819551274164e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6300000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.35999999999999943 y[1] (closed_form) 0.4291799823083151 y[1] (numeric) 0.4291799834663469 absolute error 1.1580317815784724e-09 relative error 2.698242763677089e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6400000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3499999999999994 y[1] (closed_form) 0.4330331065478039 y[1] (numeric) 0.4330331077209897 absolute error 1.1731857707530935e-09 relative error 2.709228816489073e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6500000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3399999999999994 y[1] (closed_form) 0.4368967966106436 y[1] (numeric) 0.4368967977989117 absolute error 1.188268095031475e-09 relative error 2.719791273934295e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6600000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3299999999999994 y[1] (closed_form) 0.4407710115894057 y[1] (numeric) 0.44077101279268416 absolute error 1.2032784768578608e-09 relative error 2.729940139481674e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6700000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3199999999999994 y[1] (closed_form) 0.4446557109329943 y[1] (numeric) 0.44465571215121436 absolute error 1.2182200803678711e-09 relative error 2.7396928689204355e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6800000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3099999999999994 y[1] (closed_form) 0.4485508544414789 y[1] (numeric) 0.44855085567456887 absolute error 1.2330899634704906e-09 relative error 2.7490527579217177e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.6900000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2999999999999994 y[1] (closed_form) 0.4524564022610096 y[1] (numeric) 0.4524564035089017 absolute error 1.247892122968608e-09 relative error 2.7580383805658553e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7000000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.28999999999999937 y[1] (closed_form) 0.45637231487886254 y[1] (numeric) 0.4563723161414865 absolute error 1.2626239498381153e-09 relative error 2.766653253655977e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7100000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.27999999999999936 y[1] (closed_form) 0.4602985531185597 y[1] (numeric) 0.46029855439584866 absolute error 1.2772889412815402e-09 relative error 2.7749140913604986e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7200000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.26999999999999935 y[1] (closed_form) 0.46423507813511034 y[1] (numeric) 0.46423507942699593 absolute error 1.2918855984977995e-09 relative error 2.7828263294696806e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7300000000000006 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.25999999999999934 y[1] (closed_form) 0.4681818514103284 y[1] (numeric) 0.4681818527167441 absolute error 1.3064156978437325e-09 relative error 2.790402263369135e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7400000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.24999999999999933 y[1] (closed_form) 0.4721388347482556 y[1] (numeric) 0.47213883606913554 absolute error 1.3208799609643052e-09 relative error 2.797651588369337e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7500000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.23999999999999932 y[1] (closed_form) 0.47610599027067124 y[1] (numeric) 0.47610599160594874 absolute error 1.3352774996810979e-09 relative error 2.804580339184514e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7600000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.22999999999999932 y[1] (closed_form) 0.48008328041268467 y[1] (numeric) 0.48008328176229537 absolute error 1.3496107009736136e-09 relative error 2.811201214534016e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7700000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2199999999999993 y[1] (closed_form) 0.4840706679184259 y[1] (numeric) 0.4840706692823044 absolute error 1.3638785101299788e-09 relative error 2.8175194254071507e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7800000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2099999999999993 y[1] (closed_form) 0.4880681158368061 y[1] (numeric) 0.48806811721488896 absolute error 1.3780828700404868e-09 relative error 2.823546192272212e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.7900000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1999999999999993 y[1] (closed_form) 0.4920755875173737 y[1] (numeric) 0.492075588909596 absolute error 1.3922223374152054e-09 relative error 2.8292855259072374e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8000000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.18999999999999928 y[1] (closed_form) 0.49609304660623543 y[1] (numeric) 0.49609304801253495 absolute error 1.4062995212782425e-09 relative error 2.834749511001444e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8100000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.17999999999999927 y[1] (closed_form) 0.5001204570420699 y[1] (numeric) 0.5001204584623844 absolute error 1.4203145326519007e-09 relative error 2.8399448825834067e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8200000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.16999999999999926 y[1] (closed_form) 0.5041577830522073 y[1] (numeric) 0.5041577844864747 absolute error 1.4342674825584822e-09 relative error 2.8448781924486505e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8300000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.15999999999999925 y[1] (closed_form) 0.5082049891487879 y[1] (numeric) 0.5082049905969447 absolute error 1.4481568166857528e-09 relative error 2.8495525380640725e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8400000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.14999999999999925 y[1] (closed_form) 0.5122620401249831 y[1] (numeric) 0.5122620415869701 absolute error 1.4619869759258108e-09 relative error 2.8539826522556917e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8500000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.13999999999999924 y[1] (closed_form) 0.5163289010513066 y[1] (numeric) 0.516328902527063 absolute error 1.4757564059664219e-09 relative error 2.8581712217960443e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8600000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.12999999999999923 y[1] (closed_form) 0.5204055372719747 y[1] (numeric) 0.5204055387614396 absolute error 1.489464884762981e-09 relative error 2.86212343660086e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8700000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.11999999999999922 y[1] (closed_form) 0.5244919144013411 y[1] (numeric) 0.5244919159044558 absolute error 1.5031146327615375e-09 relative error 2.865849008324949e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8800000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.10999999999999921 y[1] (closed_form) 0.5285879983204023 y[1] (numeric) 0.5285879998371071 absolute error 1.516704872805974e-09 relative error 2.869351702318877e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.8900000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.0999999999999992 y[1] (closed_form) 0.5326937551733568 y[1] (numeric) 0.5326937567035938 absolute error 1.5302369371639202e-09 relative error 2.8726391520507473e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9000000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.08999999999999919 y[1] (closed_form) 0.536809151364237 y[1] (numeric) 0.5368091529079472 absolute error 1.5437101597015612e-09 relative error 2.87571505772285e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9100000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.07999999999999918 y[1] (closed_form) 0.540934153553593 y[1] (numeric) 0.5409341551107187 absolute error 1.5571257616642242e-09 relative error 2.878586518220193e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9200000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.06999999999999917 y[1] (closed_form) 0.5450687286552434 y[1] (numeric) 0.5450687302257272 absolute error 1.5704838540742116e-09 relative error 2.881258401942821e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9300000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.059999999999999165 y[1] (closed_form) 0.5492128438330797 y[1] (numeric) 0.549212845416864 absolute error 1.583784325909221e-09 relative error 2.883735046791031e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9400000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.049999999999999156 y[1] (closed_form) 0.553366466497927 y[1] (numeric) 0.5533664680949564 absolute error 1.5970293976153016e-09 relative error 2.886024893633999e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9500000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.03999999999999915 y[1] (closed_form) 0.5575295643044678 y[1] (numeric) 0.5575295659146856 absolute error 1.6102178479471263e-09 relative error 2.8881299773867845e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9600000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.02999999999999914 y[1] (closed_form) 0.5617021051482078 y[1] (numeric) 0.5617021067715595 absolute error 1.6233516753061394e-09 relative error 2.890058022620033e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9700000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.01999999999999913 y[1] (closed_form) 0.5658840571625086 y[1] (numeric) 0.565884058798938 absolute error 1.636429436402409e-09 relative error 2.891810461330005e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9800000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.00999999999999912 y[1] (closed_form) 0.5700753887156575 y[1] (numeric) 0.5700753903651105 absolute error 1.6494529075927744e-09 relative error 2.8933943479105167e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 1.9900000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.81239525796218e-16 y[1] (closed_form) 0.5742760684080022 y[1] (numeric) 0.5742760700704242 absolute error 1.6624220888772356e-09 relative error 2.894813453546432e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.000000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.010000000000000883 y[1] (closed_form) 0.5784860650691246 y[1] (numeric) 0.5784860667444617 absolute error 1.6753370912780952e-09 relative error 2.896071647080912e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.0100000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.020000000000000892 y[1] (closed_form) 0.5827053477550685 y[1] (numeric) 0.5827053494432666 absolute error 1.6881980258176554e-09 relative error 2.8971727002705733e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.020000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.0300000000000009 y[1] (closed_form) 0.5869338857456112 y[1] (numeric) 0.586933887446618 absolute error 1.7010067798750583e-09 relative error 2.8981233170993104e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.0300000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04000000000000091 y[1] (closed_form) 0.5911716485415881 y[1] (numeric) 0.5911716502553505 absolute error 1.7137623542495817e-09 relative error 2.898925140401115e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.040000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05000000000000092 y[1] (closed_form) 0.5954186058622524 y[1] (numeric) 0.5954186075887178 absolute error 1.7264654150750403e-09 relative error 2.899582576152232e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.0500000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.06000000000000093 y[1] (closed_form) 0.5996747276426873 y[1] (numeric) 0.5996747293818041 absolute error 1.7391168505298538e-09 relative error 2.900100288311794e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.060000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000094 y[1] (closed_form) 0.6039399840312596 y[1] (numeric) 0.6039399857829764 absolute error 1.7517167716363247e-09 relative error 2.900481534512305e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.0700000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08000000000000095 y[1] (closed_form) 0.6082143453871134 y[1] (numeric) 0.608214347151379 absolute error 1.7642656224836628e-09 relative error 2.900730040099188e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.080000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000095 y[1] (closed_form) 0.6124977822777091 y[1] (numeric) 0.6124977840544719 absolute error 1.7767627369380534e-09 relative error 2.900847624836724e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.0900000000000007 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000096 y[1] (closed_form) 0.6167902654763973 y[1] (numeric) 0.6167902672656076 absolute error 1.7892103354455458e-09 relative error 2.900840748619133e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.100000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000097 y[1] (closed_form) 0.6210917659600406 y[1] (numeric) 0.621091767761648 absolute error 1.8016074188054176e-09 relative error 2.9007105190335567e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.1100000000000008 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000098 y[1] (closed_form) 0.6254022549066667 y[1] (numeric) 0.6254022567206218 absolute error 1.8139550972406937e-09 relative error 2.900461395860179e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.120000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13000000000000098 y[1] (closed_form) 0.629721703693165 y[1] (numeric) 0.6297217055194178 absolute error 1.8262527046175592e-09 relative error 2.900094905268518e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.130000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14000000000000098 y[1] (closed_form) 0.634050083893015 y[1] (numeric) 0.6340500857315171 absolute error 1.838502128315156e-09 relative error 2.8996165681848117e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.140000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.150000000000001 y[1] (closed_form) 0.6383873672740603 y[1] (numeric) 0.6383873691247616 absolute error 1.8507012589097371e-09 relative error 2.8990255036096744e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.150000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.160000000000001 y[1] (closed_form) 0.6427335257963045 y[1] (numeric) 0.6427335276591577 absolute error 1.8628532050257718e-09 relative error 2.898328981233427e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.160000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.170000000000001 y[1] (closed_form) 0.6470885316097577 y[1] (numeric) 0.647088533484715 absolute error 1.874957300529445e-09 relative error 2.89752824990597e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.170000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000102 y[1] (closed_form) 0.6514523570523068 y[1] (numeric) 0.6514523589393203 absolute error 1.887013545420757e-09 relative error 2.896625555181227e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.180000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000103 y[1] (closed_form) 0.655824974647623 y[1] (numeric) 0.6558249765466448 absolute error 1.8990218286774052e-09 relative error 2.895622920883359e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.190000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000104 y[1] (closed_form) 0.6602063571030996 y[1] (numeric) 0.6602063590140834 absolute error 1.9109838156339265e-09 relative error 2.8945250149045474e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.200000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000105 y[1] (closed_form) 0.6645964773078274 y[1] (numeric) 0.6645964792307265 absolute error 1.922899062201111e-09 relative error 2.8933332147507964e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.210000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000106 y[1] (closed_form) 0.6689953083305977 y[1] (numeric) 0.6689953102653656 absolute error 1.9347679014458663e-09 relative error 2.892050029878178e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.220000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000106 y[1] (closed_form) 0.6734028234179359 y[1] (numeric) 0.6734028253645259 absolute error 1.946590000301285e-09 relative error 2.890676921164566e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.230000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000107 y[1] (closed_form) 0.6778189959921663 y[1] (numeric) 0.6778189979505328 absolute error 1.9583664689903912e-09 relative error 2.8892174467961127e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.240000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000105 y[1] (closed_form) 0.6822437996495085 y[1] (numeric) 0.6822438016196067 absolute error 1.9700981956916053e-09 relative error 2.887674753077581e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.250000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.26000000000000106 y[1] (closed_form) 0.6866772081582018 y[1] (numeric) 0.6866772101399867 absolute error 1.981784958360322e-09 relative error 2.886050293813951e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.260000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700000000000011 y[1] (closed_form) 0.6911191954566576 y[1] (numeric) 0.6911191974500832 absolute error 1.9934256467735167e-09 relative error 2.884344205569864e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.270000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000000011 y[1] (closed_form) 0.6955697356516355 y[1] (numeric) 0.6955697376566589 absolute error 2.0050233695556585e-09 relative error 2.8825626918302855e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.280000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900000000000011 y[1] (closed_form) 0.7000288030164619 y[1] (numeric) 0.7000288050330362 absolute error 2.0165743519484636e-09 relative error 2.880701970060283e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.290000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000011 y[1] (closed_form) 0.7044963719892494 y[1] (numeric) 0.7044963740173337 absolute error 2.0280842560893575e-09 relative error 2.878771753448158e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.300000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000000011 y[1] (closed_form) 0.7089724171711769 y[1] (numeric) 0.7089724192107257 absolute error 2.0395488631308467e-09 relative error 2.876767577600146e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.310000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000011 y[1] (closed_form) 0.713456913324761 y[1] (numeric) 0.7134569153757317 absolute error 2.050970726585888e-09 relative error 2.8746945867105207e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.320000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000011 y[1] (closed_form) 0.7179498353721785 y[1] (numeric) 0.7179498374345274 absolute error 2.0623489582760612e-09 relative error 2.872553006724988e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.330000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34000000000000113 y[1] (closed_form) 0.7224511583935982 y[1] (numeric) 0.7224511604672837 absolute error 2.073685556602811e-09 relative error 2.870347057389654e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.340000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000114 y[1] (closed_form) 0.7269608576255511 y[1] (numeric) 0.7269608597105284 absolute error 2.0849773019193663e-09 relative error 2.8680736796881483e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.350000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36000000000000115 y[1] (closed_form) 0.7314789084593021 y[1] (numeric) 0.7314789105555315 absolute error 2.0962294122739422e-09 relative error 2.8657414288119177e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.360000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37000000000000116 y[1] (closed_form) 0.7360052864392785 y[1] (numeric) 0.736005288546717 absolute error 2.1074384459751627e-09 relative error 2.86334688731754e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.370000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38000000000000117 y[1] (closed_form) 0.7405399672614874 y[1] (numeric) 0.7405399693800934 absolute error 2.1186059573352622e-09 relative error 2.8608934709761245e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.3800000000000012 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000000012 y[1] (closed_form) 0.7450829267719787 y[1] (numeric) 0.7450829289017102 absolute error 2.129731502265031e-09 relative error 2.8583818334047034e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.390000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000012 y[1] (closed_form) 0.7496341409653189 y[1] (numeric) 0.7496341431061355 absolute error 2.1408166350767033e-09 relative error 2.8558152811982803e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4000000000000012 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000000012 y[1] (closed_form) 0.7541935859830957 y[1] (numeric) 0.7541935881349557 absolute error 2.1518600235026497e-09 relative error 2.8531932165634734e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.410000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000000012 y[1] (closed_form) 0.7587612381124327 y[1] (numeric) 0.7587612402752959 absolute error 2.1628632218551047e-09 relative error 2.8505188631349313e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4200000000000013 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300000000000012 y[1] (closed_form) 0.7633370737845357 y[1] (numeric) 0.7633370759583618 absolute error 2.1738260080894634e-09 relative error 2.8477930428714655e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.430000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000012 y[1] (closed_form) 0.7679210695732541 y[1] (numeric) 0.7679210717580026 absolute error 2.184748493228028e-09 relative error 2.845016994314438e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4400000000000013 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000123 y[1] (closed_form) 0.7725132021936627 y[1] (numeric) 0.7725132043892938 absolute error 2.195631121360009e-09 relative error 2.842192360111384e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.450000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46000000000000124 y[1] (closed_form) 0.7771134485006645 y[1] (numeric) 0.7771134507071392 absolute error 2.2064746696415227e-09 relative error 2.839321174918048e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4600000000000013 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47000000000000125 y[1] (closed_form) 0.7817217854876155 y[1] (numeric) 0.7817217877048941 absolute error 2.2172785829610575e-09 relative error 2.836403723324639e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.470000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48000000000000126 y[1] (closed_form) 0.7863381902849627 y[1] (numeric) 0.7863381925130061 absolute error 2.2280434164301255e-09 relative error 2.8334416971693825e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.4800000000000013 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49000000000000127 y[1] (closed_form) 0.7909626401589058 y[1] (numeric) 0.7909626423976752 absolute error 2.2387693920933316e-09 relative error 2.830436329639487e-07% Desired digits 12 Estimated correct digits 12 Correct digits 9 h 0.001 Radius of convergence (given) for eq 1 2.490000000000001 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 1500 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.06666666666676%