##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_linpostode.ode################# diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=0.001 # 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]=-1.5 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.5 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(0.0) 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 16 estimated_h 0.001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4900.0 step_error 3.571428571428571e-20 est_needed_step_err 3.571428571428571e-20 opt_iter 1 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4900.0 step_error 3.571428571428571e-20 est_needed_step_err 3.571428571428571e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.725554091601842e-113 estimated_step_error 9.725554091601842e-113 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 2450.0 step_error 5.0507627227610536e-20 est_needed_step_err 5.0507627227610536e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.680619765119502e-102 estimated_step_error 6.680619765119502e-102 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 1225.0 step_error 7.142857142857142e-20 est_needed_step_err 7.142857142857142e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.587139299919488e-91 estimated_step_error 4.587139299919488e-91 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 612.5 step_error 1.0101525445522107e-19 est_needed_step_err 1.0101525445522107e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.1471200016996604e-80 estimated_step_error 3.1471200016996604e-80 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.016 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 306.25 step_error 1.4285714285714284e-19 est_needed_step_err 1.4285714285714284e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.1556570569327156e-69 estimated_step_error 2.1556570569327156e-69 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.032 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 153.125 step_error 2.0203050891044214e-19 est_needed_step_err 2.0203050891044214e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4717915196619799e-58 estimated_step_error 1.4717915196619799e-58 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 1.6 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 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.064 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 76.5625 step_error 2.857142857142857e-19 est_needed_step_err 2.857142857142857e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.985129424249694e-48 estimated_step_error 9.985129424249694e-48 Double H and LOOP opt_iter 8 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 1.6 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 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.0 y[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Desired digits 16 Estimated correct digits -16 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 1.6 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] 0.2 y[1] (closed_form) 0.0 y[1] (numeric) -0.4519111018010179 absolute error 0.4519111018010179 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 1.7 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] 0.30000000000000004 y[1] (closed_form) 0.0 y[1] (numeric) -0.8092693172240324 absolute error 0.8092693172240324 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 1.8 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4925096023196347 Order of pole (three term test) 0.0010922044957630615 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4 y[1] (closed_form) 0.0 y[1] (numeric) -1.1047508516231863 absolute error 1.1047508516231863 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 1.9 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.63012577920383 Order of pole (three term test) 0.0032324504373753057 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5 y[1] (closed_form) 0.0 y[1] (numeric) -1.3563287277553004 absolute error 1.3563287277553004 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7618122530022244 Order of pole (three term test) 0.0073072686054369545 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6 y[1] (closed_form) 0.0 y[1] (numeric) -1.5749509079475918 absolute error 1.5749509079475918 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8888837852101317 Order of pole (three term test) 0.013895722053396444 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7 y[1] (closed_form) 0.0 y[1] (numeric) -1.7677839435859148 absolute error 1.7677839435859148 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.2 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] 0.7999999999999999 y[1] (closed_form) 0.0 y[1] (numeric) -1.9397774183651568 absolute error 1.9397774183651568 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.3 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) 0.0 y[1] (numeric) -2.0944945865622215 absolute error 2.0944945865622215 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.4 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] 0.9999999999999999 y[1] (closed_form) 0.0 y[1] (numeric) -2.2345868806921763 absolute error 2.2345868806921763 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.5 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] 1.0999999999999999 y[1] (closed_form) 0.0 y[1] (numeric) -2.3620810877927974 absolute error 2.3620810877927974 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.5999999999999996 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] 1.2 y[1] (closed_form) 0.0 y[1] (numeric) -2.4785614765442445 absolute error 2.4785614765442445 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.7 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] 1.3 y[1] (closed_form) 0.0 y[1] (numeric) -2.5852898631170356 absolute error 2.5852898631170356 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.8 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] 1.4000000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -2.68328738669675 absolute error 2.68328738669675 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 2.9000000000000004 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] 1.5000000000000002 y[1] (closed_form) 0.0 y[1] (numeric) -2.7733917778413915 absolute error 2.7733917778413915 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.0 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] 1.6000000000000003 y[1] (closed_form) 0.0 y[1] (numeric) -2.8562984399713134 absolute error 2.8562984399713134 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.1000000000000005 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] 1.7000000000000004 y[1] (closed_form) 0.0 y[1] (numeric) -2.9325905436145 absolute error 2.9325905436145 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.2 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] 1.8000000000000005 y[1] (closed_form) 0.0 y[1] (numeric) -3.002761482201959 absolute error 3.002761482201959 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.3000000000000007 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] 1.9000000000000006 y[1] (closed_form) 0.0 y[1] (numeric) -3.06723190400727 absolute error 3.06723190400727 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.4000000000000004 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] 2.0000000000000004 y[1] (closed_form) 0.0 y[1] (numeric) -3.126362819470379 absolute error 3.126362819470379 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.5000000000000004 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] 2.1000000000000005 y[1] (closed_form) 0.0 y[1] (numeric) -3.1804658202824134 absolute error 3.1804658202824134 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.6000000000000005 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] 2.2000000000000006 y[1] (closed_form) 0.0 y[1] (numeric) -3.229811140195037 absolute error 3.229811140195037 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.7000000000000006 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] 2.3000000000000007 y[1] (closed_form) 0.0 y[1] (numeric) -3.2746340804612024 absolute error 3.2746340804612024 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.8000000000000007 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] 2.400000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.3151401802705944 absolute error 3.3151401802705944 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 3.900000000000001 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] 2.500000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.3515094127379625 absolute error 3.3515094127379625 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.000000000000001 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] 2.600000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.3838996160328922 absolute error 3.3838996160328922 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.100000000000001 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] 2.700000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.4124493180525315 absolute error 3.4124493180525315 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.200000000000001 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] 2.800000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.4372800756331072 absolute error 3.4372800756331072 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.300000000000001 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] 2.9000000000000012 y[1] (closed_form) 0.0 y[1] (numeric) -3.4584984216271786 absolute error 3.4584984216271786 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.400000000000001 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] 3.0000000000000013 y[1] (closed_form) 0.0 y[1] (numeric) -3.476197492473868 absolute error 3.476197492473868 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.500000000000002 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] 3.1000000000000014 y[1] (closed_form) 0.0 y[1] (numeric) -3.4904583932380366 absolute error 3.4904583932380366 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.600000000000001 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] 3.2000000000000015 y[1] (closed_form) 0.0 y[1] (numeric) -3.501351345140954 absolute error 3.501351345140954 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.700000000000001 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] 3.3000000000000016 y[1] (closed_form) 0.0 y[1] (numeric) -3.508936651388003 absolute error 3.508936651388003 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.800000000000002 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] 3.4000000000000017 y[1] (closed_form) 0.0 y[1] (numeric) -3.513265509926099 absolute error 3.513265509926099 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 4.900000000000002 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] 3.5000000000000018 y[1] (closed_form) 0.0 y[1] (numeric) -3.514380696130838 absolute error 3.514380696130838 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.000000000000002 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] 3.600000000000002 y[1] (closed_form) 0.0 y[1] (numeric) -3.5123171339601975 absolute error 3.5123171339601975 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.100000000000001 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] 3.700000000000002 y[1] (closed_form) 0.0 y[1] (numeric) -3.5071023705426363 absolute error 3.5071023705426363 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.200000000000002 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] 3.800000000000002 y[1] (closed_form) 0.0 y[1] (numeric) -3.498756966285938 absolute error 3.498756966285938 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.3000000000000025 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] 3.900000000000002 y[1] (closed_form) 0.0 y[1] (numeric) -3.4872948102427888 absolute error 3.4872948102427888 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.400000000000002 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] 4.000000000000002 y[1] (closed_form) 0.0 y[1] (numeric) -3.472723368529943 absolute error 3.472723368529943 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.500000000000002 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] 4.100000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.4550438719774226 absolute error 3.4550438719774226 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.600000000000001 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] 4.200000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.4342514478098747 absolute error 3.4342514478098747 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.700000000000001 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] 4.300000000000001 y[1] (closed_form) 0.0 y[1] (numeric) -3.4103351989764743 absolute error 3.4103351989764743 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.800000000000001 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] 4.4 y[1] (closed_form) 0.0 y[1] (numeric) -3.3832782337021237 absolute error 3.3832782337021237 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 5.9 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] 4.5 y[1] (closed_form) 0.0 y[1] (numeric) -3.3530576468928137 absolute error 3.3530576468928137 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 6.0 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] 4.6 y[1] (closed_form) 0.0 y[1] (numeric) -3.3196444541595715 absolute error 3.3196444541595715 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 6.1 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] 4.699999999999999 y[1] (closed_form) 0.0 y[1] (numeric) -3.2830034784000826 absolute error 3.2830034784000826 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 6.199999999999999 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] 4.799999999999999 y[1] (closed_form) 0.0 y[1] (numeric) -3.243093188069306 absolute error 3.243093188069306 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 6.299999999999999 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] 4.899999999999999 y[1] (closed_form) 0.0 y[1] (numeric) -3.199865485455978 absolute error 3.199865485455978 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 6.399999999999999 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] 4.999999999999998 y[1] (closed_form) 0.0 y[1] (numeric) -3.1532654424369007 absolute error 3.1532654424369007 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 Radius of convergence (given) for eq 1 6.499999999999998 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 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 50 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.08163265306118%