##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=0.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[3 + 1] = exact_soln_y2ppp(x_start) $array_y2_init[4 + 1] = exact_soln_y2pppp(x_start) $glob_look_poles=true $glob_max_iter=200000 $glob_max_h=0.0001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) return( cos(x) ) end def exact_soln_y2 (x) return( sin(x) + 10.0 * x + 10.0) end def exact_soln_y2p (x) return( cos(x) + 10.0) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (x) return( -cos(x)) end def exact_soln_y2pppp (x) return( sin(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.4 estimated_steps 400000.00000000006 step_error 2.4999999999999997e-16 est_needed_step_err 2.4999999999999997e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4672086101164967e-183 estimated_step_error 2.4672086101164967e-183 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.65571567075937e-175 estimated_step_error 1.65571567075937e-175 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1111319777165934e-167 estimated_step_error 1.1111319777165934e-167 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.45668047786339e-160 estimated_step_error 7.45668047786339e-160 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.004093560803892e-152 estimated_step_error 5.004093560803892e-152 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.3581903421526414e-144 estimated_step_error 3.3581903421526414e-144 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2536433895763508e-136 estimated_step_error 2.2536433895763508e-136 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5123944773557834e-128 estimated_step_error 1.5123944773557834e-128 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (analytic) 11.099833416646828 y2[1] (numeric) 11.099833416646828 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 y1[1] (analytic) 0.9950041652780258 y1[1] (numeric) 0.9950041652780258 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09933466539753062 Order of pole (three term test) 22.990033288920625 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.0993346653975306 Order of pole (three term test) 22.009966711079386 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11000000000000029 y2[1] (analytic) 11.209778300837177 y2[1] (numeric) 11.209778300837177 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 y1[1] (analytic) 0.9939560979566968 y1[1] (numeric) 0.9939560979566964 absolute error 4.440892098500626e-16 relative error 4.4678956219795736e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1091148115404349 Order of pole (three term test) 22.9879487246653 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.10911481154043483 Order of pole (three term test) 22.01205127533469 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12000000000000058 y2[1] (analytic) 11.319712207288926 y2[1] (numeric) 11.319712207288916 absolute error 1.0658141036401503e-14 relative error 9.415558312108475e-14% Correct digits 16 h 0.0001 y1[1] (analytic) 0.9928086358538661 y1[1] (numeric) 0.9928086358538654 absolute error 7.771561172376096e-16 relative error 7.827854121849127e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1188513132135674 Order of pole (three term test) 22.98566898742601 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1188513132135675 Order of pole (three term test) 22.014331012573987 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13000000000000017 y2[1] (analytic) 11.429634142619697 y2[1] (numeric) 11.429634142619696 absolute error 1.7763568394002505e-15 relative error 1.5541677163369863e-14% Correct digits 16 h 0.0001 y1[1] (analytic) 0.991561893714788 y1[1] (numeric) 0.9915618937147874 absolute error 5.551115123125783e-16 relative error 5.5983546345544626e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1285402759460776 Order of pole (three term test) 22.983194989067258 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.12854027594607748 Order of pole (three term test) 22.016805010932742 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14009999999999906 y2[1] (analytic) 11.540642135545967 y2[1] (numeric) 11.540642135545976 absolute error 8.881784197001252e-15 relative error 7.696091857527364e-14% Correct digits 16 h 0.0001 y1[1] (analytic) 0.9902020369501161 y1[1] (numeric) 0.9902020369501152 absolute error 8.881784197001252e-16 relative error 8.969668679290643e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13827392706169098 Order of pole (three term test) 22.980500073980153 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.138273927061691 Order of pole (three term test) 22.019499926019837 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15009999999999796 y2[1] (analytic) 11.650537008834014 y2[1] (numeric) 11.65053700883403 absolute error 1.5987211554602254e-14 relative error 1.372229584136762e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9887561291789647 y1[1] (numeric) 0.9887561291789638 absolute error 8.881784197001252e-16 relative error 8.982785476512228e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1478556340237437 Order of pole (three term test) 22.977638682988974 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.14785563402374363 Order of pole (three term test) 22.02236131701103 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16009999999999686 y2[1] (analytic) 11.760416928545794 y2[1] (numeric) 11.760416928545828 absolute error 3.375077994860476e-14 relative error 2.869862535798561e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9872113466188561 y1[1] (numeric) 0.9872113466188553 absolute error 7.771561172376096e-16 relative error 7.872236476002084e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15737820070356873 Order of pole (three term test) 22.974586242893018 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.15737820070356862 Order of pole (three term test) 22.025413757106985 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17009999999999575 y2[1] (analytic) 11.870280906697564 y2[1] (numeric) 11.870280906697609 absolute error 4.440892098500626e-14 relative error 3.74118534633409e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9855678437467591 y1[1] (numeric) 0.9855678437467585 absolute error 5.551115123125783e-16 relative error 5.632402841008414e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16683781820146049 Order of pole (three term test) 22.971343974627636 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.16683781820146038 Order of pole (three term test) 22.02865602537236 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18009999999999465 y2[1] (analytic) 11.980127956899732 y2[1] (numeric) 11.980127956899794 absolute error 6.217248937900877e-14 relative error 5.189634835511225e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9838257849115911 y1[1] (numeric) 0.9838257849115905 absolute error 6.661338147750939e-16 relative error 6.770851353880243e-14% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17623070279654648 Order of pole (three term test) 22.967913175056907 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.17623070279654648 Order of pole (three term test) 22.03208682494309 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19009999999999355 y2[1] (analytic) 12.089957094455483 y2[1] (numeric) 12.089957094455553 absolute error 6.927791673660977e-14 relative error 5.730203688512755e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9819853443177842 y1[1] (numeric) 0.9819853443177832 absolute error 9.992007221626409e-16 relative error 1.0175311963100802e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18555309746022527 Order of pole (three term test) 22.96429521645491 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.18555309746022516 Order of pole (three term test) 22.035704783545082 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.20009999999999245 y2[1] (analytic) 12.199767336459253 y2[1] (numeric) 12.199767336459338 absolute error 8.526512829121202e-14 relative error 6.989078229090112e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9800467060078638 y1[1] (numeric) 0.9800467060078623 absolute error 1.5543122344752192e-15 relative error 1.5859573068783392e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1948012733589282 Order of pole (three term test) 22.960491545956867 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.19480127335892797 Order of pole (three term test) 22.039508454043137 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.21009999999999135 y2[1] (analytic) 12.309557701895015 y2[1] (numeric) 12.309557701895114 absolute error 9.947598300641403e-14 relative error 8.081198806282052e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9780100638440457 y1[1] (numeric) 0.9780100638440441 absolute error 1.5543122344752192e-15 relative error 1.5892599595202847e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20397153134560317 Order of pole (three term test) 22.956503684980238 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.20397153134560306 Order of pole (three term test) 22.04349631501977 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.22009999999999025 y2[1] (analytic) 12.419327211734384 y2[1] (numeric) 12.4193272117345 absolute error 1.1546319456101628e-13 relative error 9.29705712656649e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9758756214888487 y1[1] (numeric) 0.9758756214888464 absolute error 2.220446049250313e-15 relative error 2.2753371437465366e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21306020343932422 Order of pole (three term test) 22.952333228616247 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.21306020343932422 Order of pole (three term test) 22.04766677138376 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.23009999999998915 y2[1] (analytic) 12.52907488903452 y2[1] (numeric) 12.52907488903464 absolute error 1.1901590823981678e-13 relative error 9.499177656283292e-13% Correct digits 15 h 0.0001 y1[1] (analytic) 0.9736435923847299 y1[1] (numeric) 0.9736435923847273 absolute error 2.55351295663786e-15 relative error 2.6226362260378884e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22206365429243435 Order of pole (three term test) 22.947981844991833 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.22206365429243444 Order of pole (three term test) 22.052018155008163 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.24009999999998805 y2[1] (analytic) 12.638799759035813 y2[1] (numeric) 12.638799759035953 absolute error 1.4033219031261979e-13 relative error 1.1103284567214747e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9713141997327395 y1[1] (numeric) 0.9713141997327365 absolute error 2.9976021664879227e-15 relative error 3.0861302833961693e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23097828264463655 Order of pole (three term test) 22.94345127460245 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2309782826446364 Order of pole (three term test) 22.056548725397555 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.25009999999998694 y2[1] (analytic) 12.748500849259369 y2[1] (numeric) 12.748500849259518 absolute error 1.4921397450962104e-13 relative error 1.1704433036790339e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9688876764702017 y1[1] (numeric) 0.9688876764701982 absolute error 3.4416913763379853e-15 relative error 3.552208847238687e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23980052276345032 Order of pole (three term test) 22.938743329615818 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23980052276345035 Order of pole (three term test) 22.061256670384175 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.26009999999998584 y2[1] (analytic) 12.858177189604248 y2[1] (numeric) 12.858177189604419 absolute error 1.7053025658242404e-13 relative error 1.326239746643845e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9663642652474206 y1[1] (numeric) 0.966364265247417 absolute error 3.552713678800501e-15 relative error 3.676371122736923e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24852684587045637 Order of pole (three term test) 22.933859893147183 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.24852684587045631 Order of pole (three term test) 22.06614010685282 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27009999999998474 y2[1] (analytic) 12.967827812444483 y2[1] (numeric) 12.967827812444657 absolute error 1.7408297026122455e-13 relative error 1.342421975206727e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9637442184034157 y1[1] (numeric) 0.9637442184034118 absolute error 3.885780586188048e-15 relative error 4.0319625394229766e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2571537615527613 Order of pole (three term test) 22.928802918505998 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.25715376155276143 Order of pole (three term test) 22.07119708149399 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28009999999998364 y2[1] (analytic) 13.077451752725826 y2[1] (numeric) 13.077451752726008 absolute error 1.8118839761882555e-13 relative error 1.3855023214370427e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9610277979406879 y1[1] (numeric) 0.9610277979406836 absolute error 4.3298697960381105e-15 relative error 4.5054573918842446e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.26567781915911665 Order of pole (three term test) 22.923574428414717 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.26567781915911676 Order of pole (three term test) 22.076425571585286 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29009999999998254 y2[1] (analytic) 13.187048048062275 y2[1] (numeric) 13.187048048062461 absolute error 1.865174681370263e-13 relative error 1.4143989424868551e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.95821527549902 y1[1] (numeric) 0.9582152754990146 absolute error 5.329070518200751e-15 relative error 5.561454356303675e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2740956091801318 Order of pole (three term test) 22.918176514199658 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2740956091801317 Order of pole (three term test) 22.08182348580035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30009999999998144 y2[1] (analytic) 13.296615738832289 y2[1] (numeric) 13.296615738832495 absolute error 2.0605739337042905e-13 relative error 1.5496980390931042e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9553069323283122 y1[1] (numeric) 0.9553069323283064 absolute error 5.773159728050814e-15 relative error 6.043251161153242e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2824037646120337 Order of pole (three term test) 22.912611334954516 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.28240376461203354 Order of pole (three term test) 22.087388665045477 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31009999999998034 y2[1] (analytic) 13.406153868274764 y2[1] (numeric) 13.406153868274986 absolute error 2.220446049250313e-13 relative error 1.6562886500243205e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9523030592604581 y1[1] (numeric) 0.9523030592604516 absolute error 6.5503158452884236e-15 relative error 6.878394206120985e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2905989623034249 Order of pole (three term test) 22.906881116676818 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29059896230342486 Order of pole (three term test) 22.093118883323186 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.32009999999997923 y2[1] (analytic) 13.515661482584708 y2[1] (numeric) 13.515661482584942 absolute error 2.3447910280083306e-13 relative error 1.7348696037035677e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9492039566802611 y1[1] (numeric) 0.9492039566802544 absolute error 6.772360450213455e-15 relative error 7.134778993019644e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.298677924284496 Order of pole (three term test) 22.90098815137745 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.298677924284496 Order of pole (three term test) 22.099011848622553 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.33009999999997813 y2[1] (analytic) 13.62513763100861 y2[1] (numeric) 13.625137631008851 absolute error 2.4158453015843406e-13 relative error 1.7730795585405814e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9460099344953968 y1[1] (numeric) 0.9460099344953896 absolute error 7.216449660063518e-15 relative error 7.628302195275341e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3066374190781721 Order of pole (three term test) 22.894934796163977 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.306637419078172 Order of pole (three term test) 22.105065203836027 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.34009999999997703 y2[1] (analytic) 13.734581365939523 y2[1] (numeric) 13.73458136593978 absolute error 2.575717417130363e-13 relative error 1.8753519663277843e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9427213121054221 y1[1] (numeric) 0.9427213121054143 absolute error 7.771561172376096e-15 relative error 8.243752498837135e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3144742629926611 Order of pole (three term test) 22.88872347229775 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.314474262992661 Order of pole (three term test) 22.111276527702245 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.35009999999997593 y2[1] (analytic) 13.843991743011827 y2[1] (numeric) 13.84399174301209 absolute error 2.6290081223123707e-13 relative error 1.8990246246278224e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9393384183698352 y1[1] (numeric) 0.9393384183698268 absolute error 8.43769498715119e-15 relative error 8.982593304119613e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3221853213948878 Order of pole (three term test) 22.88235666422553 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3221853213948877 Order of pole (three term test) 22.117643335774467 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.36009999999997483 y2[1] (analytic) 13.953367821195656 y2[1] (numeric) 13.953367821195938 absolute error 2.824407374646398e-13 relative error 2.024176106327552e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9358615915751908 y1[1] (numeric) 0.9358615915751819 absolute error 8.881784197001252e-15 relative error 9.4904890605158e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.32976750996430326 Order of pole (three term test) 22.875836918585627 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.32976750996430326 Order of pole (three term test) 22.124163081414366 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.37009999999997373 y2[1] (analytic) 14.062708662891001 y2[1] (numeric) 14.062708662891296 absolute error 2.948752353404416e-13 relative error 2.096859448696147e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9322911794012709 y1[1] (numeric) 0.9322911794012618 absolute error 9.103828801926284e-15 relative error 9.765005829801883e-13% Correct digits 15 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33721779592657447 Order of pole (three term test) 22.869166843189394 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3372177959265744 Order of pole (three term test) 22.130833156810603 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800999999999726 y2[1] (analytic) 14.172013334021484 y2[1] (numeric) 14.172013334021782 absolute error 2.984279490192421e-13 relative error 2.1057554913727945e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9286275388863178 y1[1] (numeric) 0.9286275388863074 absolute error 1.0325074129013956e-14 relative error 1.111863874013104e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34453319926665316 Order of pole (three term test) 22.86234910597804 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3445331992666531 Order of pole (three term test) 22.13765089402196 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3900999999999715 y2[1] (analytic) 14.28128090412774 y2[1] (numeric) 14.281280904128044 absolute error 3.0375701953744283e-13 relative error 2.1269592102879753e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9248710363913296 y1[1] (numeric) 0.9248710363913184 absolute error 1.1213252548714081e-14 relative error 1.212412553480543e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.351710793920739 Order of pole (three term test) 22.855386433955548 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.351710793920739 Order of pole (three term test) 22.144613566044452 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4000999999999704 y2[1] (analytic) 14.390510446460482 y2[1] (numeric) 14.390510446460802 absolute error 3.197442310920451e-13 relative error 2.2219102809566426e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9210220475634256 y1[1] (numeric) 0.9210220475634139 absolute error 1.176836406102666e-14 relative error 1.2777505264027067e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3587477089466716 Order of pole (three term test) 22.8482816120979 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3587477089466716 Order of pole (three term test) 22.151718387902093 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4100999999999693 y2[1] (analytic) 14.49970103807317 y2[1] (numeric) 14.499701038073512 absolute error 3.4283687000424834e-13 relative error 2.3644409571206382e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9170809572982812 y1[1] (numeric) 0.917080957298269 absolute error 1.2212453270876722e-14 relative error 1.3316657786521471e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.36564112967226414 Order of pole (three term test) 22.841037482239113 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3656411296722641 Order of pole (three term test) 22.15896251776089 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4200999999999682 y2[1] (analytic) 14.608851759914302 y2[1] (numeric) 14.608851759914659 absolute error 3.5704772471945034e-13 relative error 2.444050570073995e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9130481597016386 y1[1] (numeric) 0.9130481597016253 absolute error 1.3211653993039363e-14 relative error 1.4469832563220546e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37238829882113816 Order of pole (three term test) 22.833656941934525 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37238829882113816 Order of pole (three term test) 22.166343058065475 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4300999999999671 y2[1] (analytic) 14.717961696919314 y2[1] (numeric) 14.717961696919682 absolute error 3.6770586575585185e-13 relative error 2.4983477558092713e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.9089240580498966 y1[1] (numeric) 0.9089240580498827 absolute error 1.3877787807814457e-14 relative error 1.5268368886163443e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3789865176155946 Order of pole (three term test) 22.826142943301864 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37898651761559443 Order of pole (three term test) 22.173857056698136 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.440099999999966 y2[1] (analytic) 14.827029938102104 y2[1] (numeric) 14.82702993810249 absolute error 3.8546943414985435e-13 relative error 2.5997751117996014e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.904709064749784 y1[1] (numeric) 0.9047090647497693 absolute error 1.4654943925052066e-14 relative error 1.6198515629005215e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38543314685609154 Order of pole (three term test) 22.818498491840405 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.38543314685609154 Order of pole (three term test) 22.181501508159602 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4500999999999649 y2[1] (analytic) 14.936055576646105 y2[1] (numeric) 14.93605557664651 absolute error 4.050093593832571e-13 relative error 2.7116219359582892e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.900403601297118 y1[1] (numeric) 0.900403601297103 absolute error 1.509903313490213e-14 relative error 1.6769183411917187e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39172560797688555 Order of pole (three term test) 22.810726645228794 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3917256079768854 Order of pole (three term test) 22.189273354771206 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4600999999999638 y2[1] (analytic) 15.04503770999499 y2[1] (numeric) 15.0450377099954 absolute error 4.1033842990145786e-13 relative error 2.727400474568797e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.8960080982346562 y1[1] (numeric) 0.89600809823464 absolute error 1.6209256159527285e-14 relative error 1.8090524172117729e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3978613840774277 Order of pole (three term test) 22.80283051210206 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39786138407742755 Order of pole (three term test) 22.19716948789794 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4700999999999627 y2[1] (analytic) 15.1539754399429 y2[1] (numeric) 15.153975439943327 absolute error 4.263256414560601e-13 relative error 2.8132924138991903e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.891522995109042 y1[1] (numeric) 0.8915229951090253 absolute error 1.6653345369377348e-14 relative error 1.8679658809406797e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.40383802092908644 Order of pole (three term test) 22.794813250808165 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4038380209290865 Order of pole (three term test) 22.205186749191835 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4800999999999616 y2[1] (analytic) 15.2628678727243 y2[1] (numeric) 15.26286787272474 absolute error 4.405364961712621e-13 relative error 2.8863284400078466e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.8869487404268501 y1[1] (numeric) 0.8869487404268325 absolute error 1.765254609153999e-14 relative error 1.990255500339803e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4096531279568087 Order of pole (three term test) 22.786678068144745 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4096531279568086 Order of pole (three term test) 22.21332193185526 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900999999999605 y2[1] (analytic) 15.371714119103313 y2[1] (numeric) 15.371714119103762 absolute error 4.4941828036826337e-13 relative error 2.9236705606549463e-12% Correct digits 14 h 0.0001 y1[1] (analytic) 0.8822857916097371 y1[1] (numeric) 0.8822857916097188 absolute error 1.8318679906315083e-14 relative error 2.0762750664829947e-12% Correct digits 14 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41530437919531693 Order of pole (three term test) 22.778428218076392 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4153043791953169 Order of pole (three term test) 22.22157178192361 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ; Iterations 4001 Total Elapsed Time 1 Minutes 17 Seconds Elapsed Time(since restart) 1 Minutes 17 Seconds Time to Timeout 8 Minutes 43.0 Seconds Percent Done 100.04999999998986%