##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(0.5); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); 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_y1 (double x) { return(c(1.0) + cos(c(x))); } double exact_soln_y2 (double x) { return(c(1.0) - sin(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 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] = 0.11 y2[1] (closed_form) = 0.8902216991628251 y2[1] (numeric) = 0.8902216991628249 absolute error = 2.220446049250313e-16 relative error = 2.494261880314136e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.993956097956697 y1[1] (numeric) = 1.993956097956697 absolute error = 2.220446049250313e-16 relative error = 1.113588233725763e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (closed_form) = 0.8802877927110806 y2[1] (numeric) = 0.8802877927110802 absolute error = 4.440892098500626e-16 relative error = 5.044818450592978e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.992808635853866 y1[1] (numeric) = 1.992808635853866 absolute error = 2.220446049250313e-16 relative error = 1.114229439445855e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (closed_form) = 0.8703658573803051 y2[1] (numeric) = 0.8703658573803046 absolute error = 5.551115123125783e-16 relative error = 6.37791002031486e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.991561893714788 y1[1] (numeric) = 1.991561893714788 absolute error = 2.220446049250313e-16 relative error = 1.114926960722569e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (closed_form) = 0.8604568853557635 y2[1] (numeric) = 0.8604568853557629 absolute error = 5.551115123125783e-16 relative error = 6.451357665446103e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.990215996212637 y1[1] (numeric) = 1.990215996212637 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 y2[1] (closed_form) = 0.8505618675264007 y2[1] (numeric) = 0.8505618675264002 absolute error = 5.551115123125783e-16 relative error = 6.526409582961325e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.988771077936042 y1[1] (numeric) = 1.988771077936042 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] = 0.1600000000000001 y2[1] (closed_form) = 0.840681793385754 y2[1] (numeric) = 0.8406817933857534 absolute error = 5.551115123125783e-16 relative error = 6.603110911643837e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.987227283375627 y1[1] (numeric) = 1.987227283375627 absolute error = 2.220446049250313e-16 relative error = 1.117358878788402e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y2[1] (closed_form) = 0.8308176509330039 y2[1] (numeric) = 0.8308176509330035 absolute error = 3.33066907387547e-16 relative error = 4.008905046895845e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.985584766909561 y1[1] (numeric) = 1.985584766909561 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] = 0.1800000000000001 y2[1] (closed_form) = 0.8209704265741757 y2[1] (numeric) = 0.8209704265741753 absolute error = 4.440892098500626e-16 relative error = 5.409320427085306e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.983843692788121 y1[1] (numeric) = 1.983843692788121 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] = 0.1900000000000001 y2[1] (closed_form) = 0.8111411050234993 y2[1] (numeric) = 0.811141105023499 absolute error = 3.33066907387547e-16 relative error = 4.106152497078764e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.98200423511727 y1[1] (numeric) = 1.98200423511727 absolute error = 4.440892098500626e-16 relative error = 2.240606765523823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (closed_form) = 0.8013306692049387 y2[1] (numeric) = 0.8013306692049383 absolute error = 3.33066907387547e-16 relative error = 4.156422812545139e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.980066577841242 y1[1] (numeric) = 1.980066577841241 absolute error = 6.661338147750939e-16 relative error = 3.364199074060142e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (closed_form) = 0.7915401001539003 y2[1] (numeric) = 0.7915401001539 absolute error = 3.33066907387547e-16 relative error = 4.207833656472847e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.978030914724148 y1[1] (numeric) = 1.978030914724147 absolute error = 8.881784197001252e-16 relative error = 4.49021505725045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (closed_form) = 0.7817703769191305 y2[1] (numeric) = 0.7817703769191302 absolute error = 3.33066907387547e-16 relative error = 4.260418624457559e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.975897449330605 y1[1] (numeric) = 1.975897449330604 absolute error = 1.110223024625157e-15 relative error = 5.61882918064031e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (closed_form) = 0.7720224764648115 y2[1] (numeric) = 0.7720224764648111 absolute error = 3.33066907387547e-16 relative error = 4.314212572057519e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.973666395005375 y1[1] (numeric) = 1.973666395005373 absolute error = 1.332267629550188e-15 relative error = 6.750216920760612e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (closed_form) = 0.7622973735728653 y2[1] (numeric) = 0.7622973735728651 absolute error = 2.220446049250313e-16 relative error = 2.912834447852218e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.971337974852029 y1[1] (numeric) = 1.971337974852028 absolute error = 1.554312234475219e-15 relative error = 7.884554826738359e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (closed_form) = 0.7525960407454769 y2[1] (numeric) = 0.7525960407454767 absolute error = 2.220446049250313e-16 relative error = 2.950382315393091e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.968912421710645 y1[1] (numeric) = 1.968912421710643 absolute error = 1.332267629550188e-15 relative error = 6.766515436947051e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (closed_form) = 0.7429194481078447 y2[1] (numeric) = 0.7429194481078446 absolute error = 1.110223024625157e-16 relative error = 1.494405655219828e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.966389978134513 y1[1] (numeric) = 1.966389978134512 absolute error = 1.554312234475219e-15 relative error = 7.904394610217519e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (closed_form) = 0.7332685633111687 y2[1] (numeric) = 0.7332685633111684 absolute error = 3.33066907387547e-16 relative error = 4.542222646004901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.963770896365891 y1[1] (numeric) = 1.963770896365889 absolute error = 1.332267629550188e-15 relative error = 6.78423146007333e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (closed_form) = 0.7236443514358861 y2[1] (numeric) = 0.7236443514358858 absolute error = 3.33066907387547e-16 relative error = 4.602632587771346e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.961055438310771 y1[1] (numeric) = 1.961055438310769 absolute error = 1.332267629550188e-15 relative error = 6.793625532064443e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (closed_form) = 0.7140477748951644 y2[1] (numeric) = 0.7140477748951638 absolute error = 5.551115123125783e-16 relative error = 7.774150859780763e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.958243875512697 y1[1] (numeric) = 1.958243875512695 absolute error = 1.554312234475219e-15 relative error = 7.937276117195962e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (closed_form) = 0.7044797933386603 y2[1] (numeric) = 0.7044797933386596 absolute error = 6.661338147750939e-16 relative error = 9.455683769411786e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.955336489125606 y1[1] (numeric) = 1.955336489125604 absolute error = 1.77635683940025e-15 relative error = 9.084660616110159e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (closed_form) = 0.6949413635565563 y2[1] (numeric) = 0.6949413635565559 absolute error = 4.440892098500626e-16 relative error = 6.390311947720483e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.952333569885713 y1[1] (numeric) = 1.952333569885712 absolute error = 1.554312234475219e-15 relative error = 7.961304658436039e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (closed_form) = 0.6854334393838821 y2[1] (numeric) = 0.6854334393838818 absolute error = 3.33066907387547e-16 relative error = 4.859215909963948e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.949235418082441 y1[1] (numeric) = 1.94923541808244 absolute error = 1.332267629550188e-15 relative error = 6.834821577687139e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (closed_form) = 0.6759569716051315 y2[1] (numeric) = 0.6759569716051311 absolute error = 3.33066907387547e-16 relative error = 4.927338889584115e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.946042343528387 y1[1] (numeric) = 1.946042343528386 absolute error = 1.110223024625157e-15 relative error = 5.705030151667723e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (closed_form) = 0.6665129078591854 y2[1] (numeric) = 0.666512907859185 absolute error = 3.33066907387547e-16 relative error = 4.997156145967907e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.942754665528346 y1[1] (numeric) = 1.942754665528345 absolute error = 1.332267629550188e-15 relative error = 6.857621567918707e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (closed_form) = 0.6571021925445484 y2[1] (numeric) = 0.657102192544548 absolute error = 3.33066907387547e-16 relative error = 5.068723117446707e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.939372712847379 y1[1] (numeric) = 1.939372712847378 absolute error = 1.332267629550188e-15 relative error = 6.869580151997488e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (closed_form) = 0.6477257667249099 y2[1] (numeric) = 0.6477257667249096 absolute error = 3.33066907387547e-16 relative error = 5.14209754340375e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.935896823677935 y1[1] (numeric) = 1.935896823677934 absolute error = 1.110223024625157e-15 relative error = 5.734928695816997e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (closed_form) = 0.6383845680350377 y2[1] (numeric) = 0.6383845680350375 absolute error = 2.220446049250313e-16 relative error = 3.478226386463095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.932327345606034 y1[1] (numeric) = 1.932327345606034 absolute error = 6.661338147750939e-16 relative error = 3.447313501461497e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (closed_form) = 0.6290795305870172 y2[1] (numeric) = 0.6290795305870168 absolute error = 3.33066907387547e-16 relative error = 5.294511920881451e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.92866463557651 y1[1] (numeric) = 1.928664635576509 absolute error = 6.661338147750939e-16 relative error = 3.45386026418209e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (closed_form) = 0.6198115848768384 y2[1] (numeric) = 0.619811584876838 absolute error = 4.440892098500626e-16 relative error = 7.164906572991964e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.924909059857313 y1[1] (numeric) = 1.924909059857312 absolute error = 8.881784197001252e-16 relative error = 4.614131847693433e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (closed_form) = 0.6105816576913493 y2[1] (numeric) = 0.6105816576913489 absolute error = 4.440892098500626e-16 relative error = 7.273215699423302e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.921060994002885 y1[1] (numeric) = 1.921060994002884 absolute error = 6.661338147750939e-16 relative error = 3.467530790821385e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (closed_form) = 0.6013906720155768 y2[1] (numeric) = 0.6013906720155764 absolute error = 4.440892098500626e-16 relative error = 7.384371432993561e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.917120822816605 y1[1] (numeric) = 1.917120822816605 absolute error = 4.440892098500626e-16 relative error = 2.316438299374441e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (closed_form) = 0.5922395469404296 y2[1] (numeric) = 0.5922395469404291 absolute error = 4.440892098500626e-16 relative error = 7.498472740367865e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.913088940312308 y1[1] (numeric) = 1.913088940312308 absolute error = 4.440892098500626e-16 relative error = 2.321320250680901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (closed_form) = 0.5831291975707891 y2[1] (numeric) = 0.5831291975707886 absolute error = 4.440892098500626e-16 relative error = 7.615622947711383e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.908965749674885 y1[1] (numeric) = 1.908965749674885 absolute error = 4.440892098500626e-16 relative error = 2.326334089156368e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (closed_form) = 0.5740605349340002 y2[1] (numeric) = 0.5740605349339998 absolute error = 4.440892098500626e-16 relative error = 7.735929972979584e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.904751663219963 y1[1] (numeric) = 1.904751663219963 absolute error = 4.440892098500626e-16 relative error = 2.331480887641459e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (closed_form) = 0.5650344658887696 y2[1] (numeric) = 0.5650344658887692 absolute error = 4.440892098500626e-16 relative error = 7.859506572781071e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.900447102352677 y1[1] (numeric) = 1.900447102352676 absolute error = 4.440892098500626e-16 relative error = 2.336761750960067e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (closed_form) = 0.55605189303448 y2[1] (numeric) = 0.5560518930344795 absolute error = 4.440892098500626e-16 relative error = 7.986470604867185e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.896052497525525 y1[1] (numeric) = 1.896052497525524 absolute error = 8.881784197001252e-16 relative error = 4.684355632870173e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (closed_form) = 0.5471137146209315 y2[1] (numeric) = 0.5471137146209312 absolute error = 3.33066907387547e-16 relative error = 6.087708980541876e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.891568288195329 y1[1] (numeric) = 1.891568288195328 absolute error = 8.881784197001252e-16 relative error = 4.695460508843175e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (closed_form) = 0.5382208244585168 y2[1] (numeric) = 0.5382208244585166 absolute error = 2.220446049250313e-16 relative error = 4.125529798079103e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.886994922779284 y1[1] (numeric) = 1.886994922779283 absolute error = 8.881784197001252e-16 relative error = 4.706840537715705e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (closed_form) = 0.5293741118288418 y2[1] (numeric) = 0.5293741118288415 absolute error = 2.220446049250313e-16 relative error = 4.194474190623496e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.882332858610121 y1[1] (numeric) = 1.88233285861012 absolute error = 8.881784197001252e-16 relative error = 4.718498195669491e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 Finished! diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations = 400 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100.3 %