##############ECHO OF PROBLEM################# ##############temp/lin_sinhpostode.ode################# diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(2.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.000000001; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 6.14332310027193 y[1] (numeric) = 6.14332310027193 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 6.267018809899617 y[1] (numeric) = 6.267018809899617 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 6.393221410612629 y[1] (numeric) = 6.393221410612629 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 6.521981385133975 y[1] (numeric) = 6.521981385133976 absolute error = 8.881784197001252e-16 relative error = 1.361822990977274e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 6.653350239170286 y[1] (numeric) = 6.653350239170286 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 6.787380522014783 y[1] (numeric) = 6.787380522014784 absolute error = 8.881784197001252e-16 relative error = 1.308573192293153e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 6.924125847567701 y[1] (numeric) = 6.924125847567701 absolute error = 8.881784197001252e-16 relative error = 1.282730035896334e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 7.063640915782555 y[1] (numeric) = 7.063640915782555 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 7.205981534546856 y[1] (numeric) = 7.205981534546856 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 7.351204642006011 y[1] (numeric) = 7.351204642006011 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 7.499368329339338 y[1] (numeric) = 7.499368329339338 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 7.65053186399731 y[1] (numeric) = 7.650531863997311 absolute error = 8.881784197001252e-16 relative error = 1.16093682830054e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 7.804755713409333 y[1] (numeric) = 7.804755713409334 absolute error = 8.881784197001252e-16 relative error = 1.137996437446656e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 7.962101569171518 y[1] (numeric) = 7.962101569171518 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 8.122632371724141 y[1] (numeric) = 8.122632371724141 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 8.286412335528658 y[1] (numeric) = 8.286412335528661 absolute error = 3.552713678800501e-15 relative error = 4.287396686220834e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 8.453506974754365 y[1] (numeric) = 8.453506974754365 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 8.623983129484897 y[1] (numeric) = 8.623983129484902 absolute error = 5.329070518200751e-15 relative error = 6.17936101936583e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 8.797908992455204 y[1] (numeric) = 8.797908992455204 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 8.975354136329502 y[1] (numeric) = 8.975354136329507 absolute error = 5.329070518200751e-15 relative error = 5.937448748267543e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 9.156389541531325 y[1] (numeric) = 9.156389541531325 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 9.341087624636573 y[1] (numeric) = 9.341087624636581 absolute error = 7.105427357601002e-15 relative error = 7.606638159416096e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 9.52952226734118 y[1] (numeric) = 9.529522267341184 absolute error = 3.552713678800501e-15 relative error = 3.728113098571666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 9.721768846014706 y[1] (numeric) = 9.721768846014715 absolute error = 8.881784197001252e-15 relative error = 9.135975497547658e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 9.917904261851962 y[1] (numeric) = 9.917904261851966 absolute error = 3.552713678800501e-15 relative error = 3.582121368589522e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 10.11800697163443 y[1] (numeric) = 10.11800697163444 absolute error = 5.329070518200751e-15 relative error = 5.26691722306642e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 10.32215701911413 y[1] (numeric) = 10.32215701911413 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 10.53043606703205 y[1] (numeric) = 10.53043606703206 absolute error = 7.105427357601002e-15 relative error = 6.747514834495956e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 10.74292742978449 y[1] (numeric) = 10.74292742978449 absolute error = 1.77635683940025e-15 relative error = 1.653512835314653e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 10.95971610674977 y[1] (numeric) = 10.95971610674978 absolute error = 7.105427357601002e-15 relative error = 6.483222091149767e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 11.18088881628926 y[1] (numeric) = 11.18088881628926 absolute error = 1.77635683940025e-15 relative error = 1.588743854435172e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 11.40653403043575 y[1] (numeric) = 11.40653403043576 absolute error = 8.881784197001252e-15 relative error = 7.786575811111616e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 11.63674201028358 y[1] (numeric) = 11.63674201028359 absolute error = 3.552713678800501e-15 relative error = 3.053014044361307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 11.87160484209415 y[1] (numeric) = 11.87160484209415 absolute error = 8.881784197001252e-15 relative error = 7.48153624984919e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 12.11121647413173 y[1] (numeric) = 12.11121647413173 absolute error = 1.77635683940025e-15 relative error = 1.466703896503179e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 12.355672754244 y[1] (numeric) = 12.35567275424401 absolute error = 1.243449787580175e-14 relative error = 1.00637967054693e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 12.60507146820247 y[1] (numeric) = 12.60507146820248 absolute error = 5.329070518200751e-15 relative error = 4.22771939980178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 12.85951237881808 y[1] (numeric) = 12.85951237881809 absolute error = 8.881784197001252e-15 relative error = 6.906781482345428e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 13.11909726584768 y[1] (numeric) = 13.11909726584768 absolute error = 5.329070518200751e-15 relative error = 4.062071048191455e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 13.38392996670723 y[1] (numeric) = 13.38392996670724 absolute error = 8.881784197001252e-15 relative error = 6.63615561280943e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 13.65411641800826 y[1] (numeric) = 13.65411641800826 absolute error = 1.77635683940025e-15 relative error = 1.300967990178723e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 13.92976469793379 y[1] (numeric) = 13.92976469793379 absolute error = 8.881784197001252e-15 relative error = 6.376119331232275e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 14.21098506947117 y[1] (numeric) = 14.21098506947117 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 14.49789002451867 y[1] (numeric) = 14.49789002451867 absolute error = 7.105427357601002e-15 relative error = 4.901007902242591e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 14.79059432888376 y[1] (numeric) = 14.79059432888376 absolute error = 1.77635683940025e-15 relative error = 1.20100436797952e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 15.08921506819094 y[1] (numeric) = 15.08921506819095 absolute error = 1.06581410364015e-14 relative error = 7.063416478746841e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 15.39387169471763 y[1] (numeric) = 15.39387169471763 absolute error = 1.77635683940025e-15 relative error = 1.1539376672925e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 15.70468607517656 y[1] (numeric) = 15.70468607517656 absolute error = 7.105427357601002e-15 relative error = 4.524399484069993e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 16.02178253946417 y[1] (numeric) = 16.02178253946417 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 16.34528793039417 y[1] (numeric) = 16.34528793039417 absolute error = 3.552713678800501e-15 relative error = 2.173539979185198e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 16.67533165443642 y[1] (numeric) = 16.67533165443642 absolute error = 7.105427357601002e-15 relative error = 4.261041102418268e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 17.01204573348116 y[1] (numeric) = 17.01204573348115 absolute error = 3.552713678800501e-15 relative error = 2.088351826969556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 17.35556485764959 y[1] (numeric) = 17.35556485764959 absolute error = 7.105427357601002e-15 relative error = 4.094034055289899e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 17.70602643917169 y[1] (numeric) = 17.7060264391717 absolute error = 3.552713678800501e-15 relative error = 2.00649970280215e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 18.06357066735298 y[1] (numeric) = 18.06357066735297 absolute error = 1.06581410364015e-14 relative error = 5.900351172353974e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 18.42834056465201 y[1] (numeric) = 18.42834056465201 absolute error = 3.552713678800501e-15 relative error = 1.927853279212277e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 18.80048204389141 y[1] (numeric) = 18.80048204389139 absolute error = 1.77635683940025e-14 relative error = 9.448464327952797e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 19.18014396662478 y[1] (numeric) = 19.18014396662477 absolute error = 7.105427357601002e-15 relative error = 3.704574569390669e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 19.56747820268347 y[1] (numeric) = 19.56747820268346 absolute error = 1.4210854715202e-14 relative error = 7.262486544256447e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 19.96263969092641 y[1] (numeric) = 19.9626396909264 absolute error = 1.06581410364015e-14 relative error = 5.339043934778791e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 20.36578650121782 y[1] (numeric) = 20.3657865012178 absolute error = 1.4210854715202e-14 relative error = 6.977807959615128e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 20.77707989765714 y[1] (numeric) = 20.77707989765713 absolute error = 7.105427357601002e-15 relative error = 3.419839261628976e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 21.19668440308697 y[1] (numeric) = 21.19668440308694 absolute error = 2.131628207280301e-14 relative error = 1.005642281945691e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 21.62476786490423 y[1] (numeric) = 21.62476786490422 absolute error = 1.06581410364015e-14 relative error = 4.928673039630201e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 22.06150152220157 y[1] (numeric) = 22.06150152220154 absolute error = 2.842170943040401e-14 relative error = 1.288294425554029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 22.50706007426503 y[1] (numeric) = 22.50706007426501 absolute error = 2.131628207280301e-14 relative error = 9.470931344416864e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 22.96162175045636 y[1] (numeric) = 22.96162175045633 absolute error = 3.552713678800501e-14 relative error = 1.547239875915947e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 23.4253683815069 y[1] (numeric) = 23.42536838150687 absolute error = 2.486899575160351e-14 relative error = 1.061626666722402e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 23.89848547225246 y[1] (numeric) = 23.89848547225242 absolute error = 3.907985046680551e-14 relative error = 1.63524381125237e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 24.38116227583762 y[1] (numeric) = 24.3811622758376 absolute error = 2.842170943040401e-14 relative error = 1.165724140172377e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 24.87359186941964 y[1] (numeric) = 24.8735918694196 absolute error = 4.263256414560601e-14 relative error = 1.713968950259242e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 25.37597123140172 y[1] (numeric) = 25.37597123140169 absolute error = 3.552713678800501e-14 relative error = 1.400030622041439e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 25.88850132022718 y[1] (numeric) = 25.88850132022714 absolute error = 4.618527782440651e-14 relative error = 1.784007395913686e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 26.41138715476533 y[1] (numeric) = 26.41138715476529 absolute error = 3.907985046680551e-14 relative error = 1.479659142392089e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 26.94483789632193 y[1] (numeric) = 26.94483789632188 absolute error = 5.329070518200751e-14 relative error = 1.977770487507067e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 27.48906693230633 y[1] (numeric) = 27.48906693230629 absolute error = 3.907985046680551e-14 relative error = 1.421650671630371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 28.04429196158945 y[1] (numeric) = 28.0442919615894 absolute error = 4.973799150320701e-14 relative error = 1.773551336982588e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 28.61073508158607 y[1] (numeric) = 28.61073508158603 absolute error = 4.618527782440651e-14 relative error = 1.614263935991335e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 29.1886228770969 y[1] (numeric) = 29.18862287709684 absolute error = 6.039613253960852e-14 relative error = 2.069166907733727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 29.77818651094537 y[1] (numeric) = 29.77818651094532 absolute error = 4.263256414560601e-14 relative error = 1.431670935701066e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 30.37966181644602 y[1] (numeric) = 30.37966181644596 absolute error = 6.394884621840902e-14 relative error = 2.104988745588679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 30.99328939174079 y[1] (numeric) = 30.99328939174074 absolute error = 4.618527782440651e-14 relative error = 1.490170250748349e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 31.61931469604165 y[1] (numeric) = 31.61931469604158 absolute error = 6.394884621840902e-14 relative error = 2.02246148701049e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 32.25798814781737 y[1] (numeric) = 32.25798814781734 absolute error = 3.552713678800501e-14 relative error = 1.101343847769032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 32.9095652249645 y[1] (numeric) = 32.90956522496444 absolute error = 6.394884621840902e-14 relative error = 1.943168977811313e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 33.57430656700164 y[1] (numeric) = 33.57430656700159 absolute error = 4.973799150320701e-14 relative error = 1.481430194364514e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 34.252478079329 y[1] (numeric) = 34.25247807932895 absolute error = 5.684341886080801e-14 relative error = 1.659541792251008e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 34.94435103959386 y[1] (numeric) = 34.94435103959383 absolute error = 3.552713678800501e-14 relative error = 1.016677538173504e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 35.65020220620548 y[1] (numeric) = 35.65020220620543 absolute error = 5.684341886080801e-14 relative error = 1.594476758701624e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 36.37031392904192 y[1] (numeric) = 36.37031392904188 absolute error = 3.552713678800501e-14 relative error = 9.768168858074214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 37.10497426239399 y[1] (numeric) = 37.10497426239395 absolute error = 4.263256414560601e-14 relative error = 1.14897166735982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 37.8544770801905 y[1] (numeric) = 37.85447708019054 absolute error = 4.263256414560601e-14 relative error = 1.126222508774686e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 38.61912219355218 y[1] (numeric) = 38.61912219355231 absolute error = 1.35003119794419e-13 relative error = 3.495758373735358e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 39.39921547071977 y[1] (numeric) = 39.39921547072 absolute error = 2.273736754432321e-13 relative error = 5.771020380144596e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 40.19506895940553 y[1] (numeric) = 40.19506895940585 absolute error = 3.197442310920451e-13 relative error = 7.954812353101482e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 41.00700101161643 y[1] (numeric) = 41.00700101161686 absolute error = 4.263256414560601e-13 relative error = 1.039641112343941e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 41.83533641099929 y[1] (numeric) = 41.83533641099981 absolute error = 5.186961971048731e-13 relative error = 1.239851861137414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 42.68040650275847 y[1] (numeric) = 42.68040650275907 absolute error = 5.968558980384842e-13 relative error = 1.398430678020625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 43.54254932619842 y[1] (numeric) = 43.54254932619912 absolute error = 7.034373084024992e-13 relative error = 1.615517050076026e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 44.42210974994391 y[1] (numeric) = 44.42210974994471 absolute error = 7.958078640513122e-13 relative error = 1.79146796163214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 45.31943960989206 y[1] (numeric) = 45.31943960989295 absolute error = 8.881784197001252e-13 relative error = 1.959817745641892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 46.23489784995142 y[1] (numeric) = 46.23489784995243 absolute error = 1.001865257421741e-12 relative error = 2.166902716370539e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 47.1688506656243 y[1] (numeric) = 47.16885066562539 absolute error = 1.094235813070554e-12 relative error = 2.319827169051654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 48.1216716504898 y[1] (numeric) = 48.121671650491 absolute error = 1.200817223434569e-12 relative error = 2.495377201681951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 49.09374194564634 y[1] (numeric) = 49.09374194564766 absolute error = 1.321609488513786e-12 relative error = 2.692012130542002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 50.08545039217308 y[1] (numeric) = 50.08545039217451 absolute error = 1.435296326235402e-12 relative error = 2.865695156970572e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 51.0971936866716 y[1] (numeric) = 51.09719368667314 absolute error = 1.541877736599417e-12 relative error = 3.017538978861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 52.12937653994979 y[1] (numeric) = 52.12937653995144 absolute error = 1.648459146963432e-12 relative error = 3.162246043169386e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 53.18241183891157 y[1] (numeric) = 53.18241183891332 absolute error = 1.755040557327447e-12 relative error = 3.300039424017529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 54.25672081171719 y[1] (numeric) = 54.25672081171907 absolute error = 1.875832822406664e-12 relative error = 3.45732804036613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 55.35273319628008 y[1] (numeric) = 55.35273319628208 absolute error = 1.996625087485882e-12 relative error = 3.607093944947351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 56.47088741216777 y[1] (numeric) = 56.47088741216989 absolute error = 2.1245227799227e-12 relative error = 3.762155824498216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 57.61163073597552 y[1] (numeric) = 57.61163073597778 absolute error = 2.259525899717119e-12 relative error = 3.921996081090203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 58.77541948024297 y[1] (numeric) = 58.77541948024537 absolute error = 2.394529019511538e-12 relative error = 4.074031356452411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 59.96271917598523 y[1] (numeric) = 59.96271917598775 absolute error = 2.522426711948356e-12 relative error = 4.206658314719282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 61.17400475891145 y[1] (numeric) = 61.17400475891412 absolute error = 2.664535259100376e-12 relative error = 4.355665890440535e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 62.40976075940551 y[1] (numeric) = 62.40976075940831 absolute error = 2.799538378894795e-12 relative error = 4.485738039739061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 63.67048149634456 y[1] (numeric) = 63.6704814963475 absolute error = 2.934541498689214e-12 relative error = 4.608951322062314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 64.95667127483321 y[1] (numeric) = 64.9566712748363 absolute error = 3.083755473198835e-12 relative error = 4.747403788829315e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 66.26884458793229 y[1] (numeric) = 66.26884458793552 absolute error = 3.225864020350855e-12 relative error = 4.867844068218887e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 67.60752632246293 y[1] (numeric) = 67.6075263224663 absolute error = 3.367972567502875e-12 relative error = 4.981653302087832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 68.97325196896824 y[1] (numeric) = 68.97325196897175 absolute error = 3.510081114654895e-12 relative error = 5.089046861577754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 70.36656783591675 y[1] (numeric) = 70.36656783592042 absolute error = 3.666400516522117e-12 relative error = 5.21042965328586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 71.78803126823304 y[1] (numeric) = 71.78803126823686 absolute error = 3.822719918389339e-12 relative error = 5.325010103851299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 73.23821087024312 y[1] (numeric) = 73.2382108702471 absolute error = 3.979039320256561e-12 relative error = 5.433009999802242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 74.7176867331238 y[1] (numeric) = 74.71768673312795 absolute error = 4.149569576838985e-12 relative error = 5.553664411025456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 76.22705066694682 y[1] (numeric) = 76.22705066695113 absolute error = 4.305888978706207e-12 relative error = 5.648767650108368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 77.76690643741085 y[1] (numeric) = 77.76690643741532 absolute error = 4.462208380573429e-12 relative error = 5.737927075914674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 79.33787000735575 y[1] (numeric) = 79.33787000736037 absolute error = 4.618527782440651e-12 relative error = 5.821340782166761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 80.94056978315594 y[1] (numeric) = 80.94056978316075 absolute error = 4.817479748453479e-12 relative error = 5.951872789331435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 82.57564686609138 y[1] (numeric) = 82.57564686609638 absolute error = 5.002220859751105e-12 relative error = 6.057743474735288e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 84.24375530879655 y[1] (numeric) = 84.24375530880174 absolute error = 5.186961971048731e-12 relative error = 6.157087788923768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 85.94556237689028 y[1] (numeric) = 85.94556237689568 absolute error = 5.400124791776761e-12 relative error = 6.283192107227155e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 87.68174881589088 y[1] (numeric) = 87.68174881589647 absolute error = 5.584865903074387e-12 relative error = 6.369473668689215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 89.4530091235234 y[1] (numeric) = 89.45300912352917 absolute error = 5.769607014372014e-12 relative error = 6.449874711766162e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 91.260051827528 y[1] (numeric) = 91.26005182753399 absolute error = 5.982769835100044e-12 relative error = 6.555737932745048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 93.10359976908052 y[1] (numeric) = 93.10359976908671 absolute error = 6.195932655828074e-12 relative error = 6.654879801850291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 94.98439039193856 y[1] (numeric) = 94.98439039194496 absolute error = 6.394884621840902e-12 relative error = 6.732563735423671e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 96.90317603742878 y[1] (numeric) = 96.90317603743539 absolute error = 6.608047442568932e-12 relative error = 6.819226895119081e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 98.86072424539354 y[1] (numeric) = 98.86072424540038 absolute error = 6.835421118012164e-12 relative error = 6.914192840672684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 100.857818061217 y[1] (numeric) = 100.8578180612241 absolute error = 7.048583938740194e-12 relative error = 6.988634172575457e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 102.8952563490538 y[1] (numeric) = 102.8952563490611 absolute error = 7.275957614183426e-12 relative error = 7.071227452411448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 104.9738541113853 y[1] (numeric) = 104.9738541113928 absolute error = 7.503331289626658e-12 relative error = 7.147809664742854e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 107.0944428150313 y[1] (numeric) = 107.094442815039 absolute error = 7.716494110354688e-12 relative error = 7.205317015078242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 109.2578707237483 y[1] (numeric) = 109.2578707237562 absolute error = 7.94386778579792e-12 relative error = 7.270751052693946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 111.4650032375458 y[1] (numeric) = 111.465003237554 absolute error = 8.199663170671556e-12 relative error = 7.356266929088992e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 113.7167232388582 y[1] (numeric) = 113.7167232388666 absolute error = 8.469669410260394e-12 relative error = 7.448042090054016e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 116.0139314457093 y[1] (numeric) = 116.013931445718 absolute error = 8.753886504564434e-12 relative error = 7.545547673005949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 118.3575467720117 y[1] (numeric) = 118.3575467720207 absolute error = 9.023892744153272e-12 relative error = 7.624264772516538e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 120.7485066951446 y[1] (numeric) = 120.7485066951539 absolute error = 9.279688129026908e-12 relative error = 7.6851369702281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 123.1877676309571 y[1] (numeric) = 123.1877676309666 absolute error = 9.521272659185342e-12 relative error = 7.729073139557931e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 125.6763053163474 y[1] (numeric) = 125.6763053163572 absolute error = 9.805489753489383e-12 relative error = 7.802178564055806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 128.2151151995707 y[1] (numeric) = 128.2151151995807 absolute error = 1.006128513836302e-11 relative error = 7.847191123060902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 130.8052128384314 y[1] (numeric) = 130.8052128384417 absolute error = 1.034550223266706e-11 relative error = 7.909090171693437e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 133.4476343065203 y[1] (numeric) = 133.4476343065309 absolute error = 1.060129761754069e-11 relative error = 7.944163021421738e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 136.1434366076573 y[1] (numeric) = 136.1434366076681 absolute error = 1.088551471184473e-11 relative error = 7.995622104953159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 138.8936980987073 y[1] (numeric) = 138.8936980987185 absolute error = 1.116973180614877e-11 relative error = 8.041928438114449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 141.6995189209375 y[1] (numeric) = 141.699518920949 absolute error = 1.148237060988322e-11 relative error = 8.103323636751307e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 144.5620214400882 y[1] (numeric) = 144.5620214400999 absolute error = 1.173816599475686e-11 relative error = 8.119813127835641e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 147.4823506953342 y[1] (numeric) = 147.4823506953462 absolute error = 1.20508047984913e-11 relative error = 8.171014864948543e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 150.4616748573159 y[1] (numeric) = 150.4616748573283 absolute error = 1.239186531165615e-11 relative error = 8.235894837278304e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 153.5011856954229 y[1] (numeric) = 153.5011856954356 absolute error = 1.2732925824821e-11 relative error = 8.2950016100108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 156.6020990545178 y[1] (numeric) = 156.6020990545309 absolute error = 1.307398633798584e-11 relative error = 8.348538376509502e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 159.7656553412904 y[1] (numeric) = 159.7656553413038 absolute error = 1.34434685605811e-11 relative error = 8.414492170963305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 162.9931200204366 y[1] (numeric) = 162.9931200204504 absolute error = 1.381295078317635e-11 relative error = 8.474560632647829e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 166.2857841208615 y[1] (numeric) = 166.2857841208757 absolute error = 1.41824330057716e-11 relative error = 8.528950974824991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 169.6449647521081 y[1] (numeric) = 169.6449647521227 absolute error = 1.452349351893645e-11 relative error = 8.561110870669662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 173.0720056312186 y[1] (numeric) = 173.0720056312335 absolute error = 1.48929757415317e-11 relative error = 8.605074915041785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 176.5682776202391 y[1] (numeric) = 176.5682776202543 absolute error = 1.523403625469655e-11 relative error = 8.62784440105472e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 180.1351792745827 y[1] (numeric) = 180.1351792745983 absolute error = 1.56319401867222e-11 relative error = 8.677894151310783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 183.7741374024706 y[1] (numeric) = 183.7741374024866 absolute error = 1.600142240931746e-11 relative error = 8.707113326982396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 187.4866076356739 y[1] (numeric) = 187.4866076356903 absolute error = 1.642774805077352e-11 relative error = 8.76209146772558e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 191.2740750117862 y[1] (numeric) = 191.2740750118031 absolute error = 1.682565198279917e-11 relative error = 8.796619187290479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 195.1380545682583 y[1] (numeric) = 195.1380545682756 absolute error = 1.728039933368564e-11 relative error = 8.85547381924987e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 199.0800919484331 y[1] (numeric) = 199.0800919484508 absolute error = 1.77351466845721e-11 relative error = 8.908548570072977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 203.1017640198238 y[1] (numeric) = 203.101764019842 absolute error = 1.818989403545856e-11 relative error = 8.956049260942479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 207.2046795048821 y[1] (numeric) = 207.2046795049007 absolute error = 1.861621967691462e-11 relative error = 8.984459096868997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 211.3904796245081 y[1] (numeric) = 211.3904796245272 absolute error = 1.909938873723149e-11 relative error = 9.03512247626177e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 215.6608387545614 y[1] (numeric) = 215.6608387545809 absolute error = 1.952571437868755e-11 relative error = 9.053898932902381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 220.0174650956325 y[1] (numeric) = 220.0174650956526 absolute error = 2.003730514843483e-11 relative error = 9.107142989637406e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 224.4621013563473 y[1] (numeric) = 224.4621013563678 absolute error = 2.052047420875169e-11 relative error = 9.142066337592637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 228.9965254504725 y[1] (numeric) = 228.9965254504935 absolute error = 2.100364326906856e-11 relative error = 9.172035788643981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 233.6225512081056 y[1] (numeric) = 233.622551208127 absolute error = 2.148681232938543e-11 relative error = 9.197233836491014e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 238.3420291012307 y[1] (numeric) = 238.3420291012528 absolute error = 2.202682480856311e-11 relative error = 9.241687205410036e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 243.1568469839325 y[1] (numeric) = 243.156846983955 absolute error = 2.253841557831038e-11 relative error = 9.26908530764083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 248.0689308475623 y[1] (numeric) = 248.0689308475854 absolute error = 2.313527147634886e-11 relative error = 9.326146324452629e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 253.0802455911609 y[1] (numeric) = 253.0802455911846 absolute error = 2.367528395552654e-11 relative error = 9.354852608201128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 258.1927958074443 y[1] (numeric) = 258.1927958074685 absolute error = 2.415845301584341e-11 relative error = 9.356749455496179e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 263.4086265846671 y[1] (numeric) = 263.4086265846919 absolute error = 2.48405740421731e-11 relative error = 9.430432998438124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 268.7298243246856 y[1] (numeric) = 268.7298243247109 absolute error = 2.529532139305957e-11 relative error = 9.412919260683611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 274.1585175775461 y[1] (numeric) = 274.158517577572 absolute error = 2.586375558166765e-11 relative error = 9.433869066042073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; Iterations = 1901 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %