##############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=30 ! #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_max_iter=1000000 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.1 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #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 10 desired_abs_gbl_error 1.0e-10 range 4.9 estimated_steps 4900000.000000001 step_error 2.040816326530612e-17 est_needed_step_err 2.040816326530612e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.322522384818648e-146 estimated_step_error 1.322522384818648e-146 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 8.875285819891103e-139 estimated_step_error 8.875285819891103e-139 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 5.956087832591041e-131 estimated_step_error 5.956087832591041e-131 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 3.997041867794536e-123 estimated_step_error 3.997041867794536e-123 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 2.682341185000824e-115 estimated_step_error 2.682341185000824e-115 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 1.800050841493786e-107 estimated_step_error 1.800050841493786e-107 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 1.2079428644070963e-99 estimated_step_error 1.2079428644070963e-99 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 8.105685510359236e-92 estimated_step_error 8.105685510359236e-92 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.438718559519279e-84 estimated_step_error 5.438718559519279e-84 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.648634896522908e-76 estimated_step_error 3.648634896522908e-76 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4469117830139833e-68 estimated_step_error 2.4469117830139833e-68 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.639890424531904e-60 estimated_step_error 1.639890424531904e-60 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0975653168776032e-52 estimated_step_error 1.0975653168776032e-52 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.326411095212077e-45 estimated_step_error 7.326411095212077e-45 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.8648897874092096e-37 estimated_step_error 4.8648897874092096e-37 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.197595714309029e-29 estimated_step_error 3.197595714309029e-29 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0619440232397655e-21 estimated_step_error 2.0619440232397655e-21 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2878450049206604e-13 estimated_step_error 1.2878450049206604e-13 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 0.0 y[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Correct digits -1 h 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.38294942485764055 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2148848274572922 y[1] (analytic) 0.0 y[1] (numeric) -0.4527817649310169 absolute error 0.4527817649310169 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5030562899266292 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.0417351517928657 Order of pole (six term test) -1.8241053112433292e-10 TOP MAIN SOLVE Loop x[1] 0.3297696549145843 y[1] (analytic) 0.0 y[1] (numeric) -0.8103457478893303 absolute error 0.8103457478893303 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6231631549956663 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.135441405325396 Order of pole (six term test) 2.326974168909146e-10 TOP MAIN SOLVE Loop x[1] 0.4063595398861124 y[1] (analytic) 0.0 y[1] (numeric) -1.012760847833521 absolute error 1.012760847833521 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7032343983752807 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.2033500659823277 Order of pole (six term test) 4.4213521732672234e-10 TOP MAIN SOLVE Loop x[1] 0.5212443673434045 y[1] (analytic) 0.0 y[1] (numeric) -1.2768659109658744 absolute error 1.2768659109658744 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8233412634475719 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.3129004825654116 Order of pole (six term test) 6.086064985311168e-10 TOP MAIN SOLVE Loop x[1] 0.6361291948006966 y[1] (analytic) 0.0 y[1] (numeric) -1.504395163472756 absolute error 1.504395163472756 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9434481285383963 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.441197807989858 Order of pole (six term test) 1.3339178650539907e-09 TOP MAIN SOLVE Loop x[1] 0.7127190797722247 y[1] (analytic) 0.0 y[1] (numeric) -1.639927012068032 absolute error 1.639927012068032 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.0235193719701021 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.5289226446896762 Order of pole (six term test) 5.233459887676872e-09 TOP MAIN SOLVE Loop x[1] 0.8276039072295168 y[1] (analytic) 0.0 y[1] (numeric) -1.8233490759129805 absolute error 1.8233490759129805 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.143626237298147 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.6587936196448434 Order of pole (six term test) 2.3002071358746434e-08 TOP MAIN SOLVE Loop x[1] 0.9041937922010449 y[1] (analytic) 0.0 y[1] (numeric) -1.9342736979531834 absolute error 1.9342736979531834 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.2236974811376835 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7444194911268383 Order of pole (six term test) 5.0628932157792406e-08 TOP MAIN SOLVE Loop x[1] 1.019078619658337 y[1] (analytic) 0.0 y[1] (numeric) -2.0861200638452506 absolute error 2.0861200638452506 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.343804347929532 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8722767402493288 Order of pole (six term test) 1.5159211308457543e-07 TOP MAIN SOLVE Loop x[1] 1.1339634471156295 y[1] (analytic) 0.0 y[1] (numeric) -2.2228116197163237 absolute error 2.2228116197163237 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4639112174062892 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9993676182382103 Order of pole (six term test) 3.9265957951784003e-07 TOP MAIN SOLVE Loop x[1] 1.2105533320871578 y[1] (analytic) 0.0 y[1] (numeric) -2.306539250723959 absolute error 2.306539250723959 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5439824665993882 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.083775894972517 Order of pole (six term test) 6.961338350208734e-07 TOP MAIN SOLVE Loop x[1] 1.3254381595444502 y[1] (analytic) 0.0 y[1] (numeric) -2.422246853114057 absolute error 2.422246853114057 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.6640893481956656 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.210001213126851 Order of pole (six term test) 1.5176530681060285e-06 TOP MAIN SOLVE Loop x[1] 1.4020280445159785 y[1] (analytic) 0.0 y[1] (numeric) -2.493380180077752 absolute error 2.493380180077752 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.7441606108820111 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.293934924103142 Order of pole (six term test) 2.4351005709633e-06 TOP MAIN SOLVE Loop x[1] 1.516912871973271 y[1] (analytic) 0.0 y[1] (numeric) -2.5919080276152884 absolute error 2.5919080276152884 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8642675250083787 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.4196016854837694 Order of pole (six term test) 4.671607792161581e-06 TOP MAIN SOLVE Loop x[1] 1.6317976994305634 y[1] (analytic) 0.0 y[1] (numeric) -2.6814595442114717 absolute error 2.6814595442114717 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.9843744764269782 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.5450650780723345 Order of pole (six term test) 8.442061121272104e-06 TOP MAIN SOLVE Loop x[1] 1.7083875844020917 y[1] (analytic) 0.0 y[1] (numeric) -2.736565653332544 absolute error 2.736565653332544 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.0644458078668873 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.628659431985594 Order of pole (six term test) 1.2193784113989636e-05 TOP MAIN SOLVE Loop x[1] 1.8232724118593842 y[1] (analytic) 0.0 y[1] (numeric) -2.8128279870958393 absolute error 2.8128279870958393 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.1845528702299246 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.7541747150728293 Order of pole (six term test) 2.0615367320786504e-05 TOP MAIN SOLVE Loop x[1] 1.9381572393166766 y[1] (analytic) 0.0 y[1] (numeric) -2.8819195008339134 absolute error 2.8819195008339134 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3046600408856506 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.8804780756335266 Order of pole (six term test) 3.4874492248704314e-05 TOP MAIN SOLVE Loop x[1] 2.014747124288205 y[1] (analytic) 0.0 y[1] (numeric) -2.9242402324195833 absolute error 2.9242402324195833 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.384731568642647 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.966067009705544 Order of pole (six term test) 5.131199652552709e-05 TOP MAIN SOLVE Loop x[1] 2.1296319517454974 y[1] (analytic) 0.0 y[1] (numeric) -2.9824248106535176 absolute error 2.9824248106535176 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5048390188968708 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.100798989864715 Order of pole (six term test) 0.00010570057042968983 TOP MAIN SOLVE Loop x[1] 2.2062218367170257 y[1] (analytic) 0.0 y[1] (numeric) -3.0178436786904492 absolute error 3.0178436786904492 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5849107840900487 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.201518636669577 Order of pole (six term test) 0.00019804003393986136 TOP MAIN SOLVE Loop x[1] 2.321106664174318 y[1] (analytic) 0.0 y[1] (numeric) -3.066156814036329 absolute error 3.066156814036329 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.705018681378098 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.4008219447599877 Order of pole (six term test) 0.0006363463677878656 TOP MAIN SOLVE Loop x[1] 2.4359914916316106 y[1] (analytic) 0.0 y[1] (numeric) -3.1089431804945624 absolute error 3.1089431804945624 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.825126951767589 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.7779470946717493 Order of pole (six term test) 0.0024888339332598264 TOP MAIN SOLVE Loop x[1] 2.512581376603139 y[1] (analytic) 0.0 y[1] (numeric) -3.134520142632891 absolute error 3.134520142632891 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.9051993876684814 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.329014319492516 Order of pole (six term test) 0.006829951648313681 TOP MAIN SOLVE Loop x[1] 2.6274662040604313 y[1] (analytic) 0.0 y[1] (numeric) -3.1686256042134335 absolute error 3.1686256042134335 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.0253085175741323 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 7.257737183860852 Order of pole (six term test) 0.048565076065330004 TOP MAIN SOLVE Loop x[1] 2.7040560890319596 y[1] (analytic) 0.0 y[1] (numeric) -3.1886054176319485 absolute error 3.1886054176319485 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.1053816640228304 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.818940916489252 y[1] (analytic) 0.0 y[1] (numeric) -3.2145646346264107 absolute error 3.2145646346264107 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.225492195912847 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9338257439465445 y[1] (analytic) 0.0 y[1] (numeric) -3.2358418419438264 absolute error 3.2358418419438264 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.345604302116959 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.010415628918073 y[1] (analytic) 0.0 y[1] (numeric) -3.2474891686750604 absolute error 3.2474891686750604 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.425680696047755 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.1253004563753652 y[1] (analytic) 0.0 y[1] (numeric) -3.2612361155752905 absolute error 3.2612361155752905 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.5458009734565454 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2018903413468935 y[1] (analytic) 0.0 y[1] (numeric) -3.267959582194494 absolute error 3.267959582194494 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.6258896411862445 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.316775168804186 y[1] (analytic) 0.0 y[1] (numeric) -3.274444172636536 absolute error 3.274444172636536 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.746056353643607 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.4316599962614784 y[1] (analytic) 0.0 y[1] (numeric) -3.2766691372968775 absolute error 3.2766691372968775 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.866334916094308 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.5082498812330067 y[1] (analytic) 0.0 y[1] (numeric) -3.275814178137301 absolute error 3.275814178137301 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.94668270169462 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.623134708690299 y[1] (analytic) 0.0 y[1] (numeric) -3.2710577146127338 absolute error 3.2710577146127338 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.067858650760485 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.7380195361475916 y[1] (analytic) 0.0 y[1] (numeric) -3.2621624195600507 absolute error 3.2621624195600507 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.18812872418229 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.81460942111912 y[1] (analytic) 0.0 y[1] (numeric) -3.2539446983132 absolute error 3.2539446983132 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.261218622141612 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.9294942485764124 y[1] (analytic) 0.0 y[1] (numeric) -3.2381968963734273 absolute error 3.2381968963734273 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.342926904596108 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.00608413354794 y[1] (analytic) 0.0 y[1] (numeric) -3.2254194800569587 absolute error 3.2254194800569587 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.35900085072192 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.120968961005231 y[1] (analytic) 0.0 y[1] (numeric) -3.2028317464931066 absolute error 3.2028317464931066 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.269180377059034 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.2358537884625225 y[1] (analytic) 0.0 y[1] (numeric) -3.1761255595518456 absolute error 3.1761255595518456 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 3.8892978334916246 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9351146568849447 Order of pole (three term test) -289.35163902127186 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.31244367343405 y[1] (analytic) 0.0 y[1] (numeric) -3.1560221473203054 absolute error 3.1560221473203054 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6994923696962628 Order of pole (three term test) -112.35915432843036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.427328500891341 y[1] (analytic) 0.0 y[1] (numeric) -3.12239410770723 absolute error 3.12239410770723 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1791299549704147 Order of pole (three term test) -40.842688359692 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.503918385862868 y[1] (analytic) 0.0 y[1] (numeric) -3.097642341253051 absolute error 3.097642341253051 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.05781463978133827 Order of pole (three term test) -27.642336419278582 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.6188032133201595 y[1] (analytic) 0.0 y[1] (numeric) -3.0569779621895843 absolute error 3.0569779621895843 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 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] 4.733688040777451 y[1] (analytic) 0.0 y[1] (numeric) -3.012016019688234 absolute error 3.012016019688234 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 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] 4.810277925748978 y[1] (analytic) 0.0 y[1] (numeric) -2.9796194832033667 absolute error 2.9796194832033667 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.052477315023725 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.925162753206269 y[1] (analytic) 0.0 y[1] (numeric) -2.9273322799709334 absolute error 2.9273322799709334 relative error -1.0% Correct digits -1 h 0.03829494248576406 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 4.50966996282147 Order of pole (ratio test) Not computed 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 128 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.81729756456247%