##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 1 ) = y1 ; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.2); x_end=c(0.8); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_max_h=0.00001; glob_look_poles=true; 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(cos(c(x))); } double exact_soln_y2 (double x) { return(sin(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y1[1] (closed_form) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412416 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 0.1986693307950612 y2[1] (numeric) = 0.1986693307950612 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] = 0.21 y1[1] (closed_form) = 0.9780309147241483 y1[1] (numeric) = 0.9780798845332912 absolute error = 4.896980914292914e-05 relative error = 0.00500697967780916 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 h = 0.001 y2[1] (closed_form) = 0.2084598998460996 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.009790569051038367 relative error = 4.696619857472101 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y1[1] (closed_form) = 0.9758974493306055 y1[1] (numeric) = 0.9760931912253408 absolute error = 0.0001957418947352574 relative error = 0.0200576295049774 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.001 y2[1] (closed_form) = 0.2182296230808694 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.01956029228580813 relative error = 8.963170081891072 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y1[1] (closed_form) = 0.9736663950053748 y1[1] (numeric) = 0.9741064979173903 absolute error = 0.0004401029120155719 relative error = 0.04520058556741527 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.001 y2[1] (closed_form) = 0.2279775235351884 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.02930819274012722 relative error = 12.85573783136717 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y1[1] (closed_form) = 0.9713379748520296 y1[1] (numeric) = 0.9721198046094399 absolute error = 0.0007818297574103683 relative error = 0.08048998161834141 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.001 y2[1] (closed_form) = 0.2377026264271346 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.03903329563207342 relative error = 16.42106198773478 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y1[1] (closed_form) = 0.9689124217106447 y1[1] (numeric) = 0.9701331113014895 absolute error = 0.001220689590844759 relative error = 0.1259855445644503 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.247403959254523 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.04873462845946178 relative error = 19.69840280903703 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y1[1] (closed_form) = 0.9663899781345132 y1[1] (numeric) = 0.9681464179935391 absolute error = 0.001756439859025849 relative error = 0.1817526980584403 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.2570805518921552 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.05841122109709396 relative error = 22.72098012361408 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y1[1] (closed_form) = 0.9637708963658905 y1[1] (numeric) = 0.9661597246855886 absolute error = 0.002388828319698111 relative error = 0.247862674490972 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.2667314366888312 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.06806210589376999 relative error = 25.51709192537782 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y1[1] (closed_form) = 0.9610554383107709 y1[1] (numeric) = 0.9641730313776382 absolute error = 0.003117593066867319 relative error = 0.3243926356992531 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.2763556485641138 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.0776863177690526 relative error = 28.11099326997457 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y1[1] (closed_form) = 0.9582438755126972 y1[1] (numeric) = 0.9621863380696878 absolute error = 0.0039424625569906 relative error = 0.4114258027353665 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.2859522251048356 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.08728289430977443 relative error = 30.52359333024068 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y1[1] (closed_form) = 0.955336489125606 y1[1] (numeric) = 0.9601996447617374 absolute error = 0.004863155636131378 relative error = 0.5090515950649487 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.2955202066613397 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.09685087586627844 relative error = 32.77301304044757 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y1[1] (closed_form) = 0.9523335698857134 y1[1] (numeric) = 0.9582129514537869 absolute error = 0.00587938156807355 relative error = 0.6173657795953907 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3050586364434436 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1063893056483824 relative error = 34.87503480928541 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y1[1] (closed_form) = 0.9492354180824408 y1[1] (numeric) = 0.9562262581458365 absolute error = 0.006990840063395676 relative error = 0.7364706299642649 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3145665606161179 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1158972298210567 relative error = 36.84346791154707 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y1[1] (closed_form) = 0.9460423435283869 y1[1] (numeric) = 0.9542395648378861 absolute error = 0.008197221309499181 relative error = 0.8664750965508148 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3240430283948685 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1253736975998073 relative error = 38.69044744484701 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y1[1] (closed_form) = 0.9427546655283462 y1[1] (numeric) = 0.9522528715299357 absolute error = 0.00949820600158946 relative error = 1.007494987708854 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3334870921408145 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1348177613457533 relative error = 40.42668052916023 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y1[1] (closed_form) = 0.9393727128473789 y1[1] (numeric) = 0.9502661782219852 absolute error = 0.01089346537460634 relative error = 1.159653162756518 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3428978074554515 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1442284766603903 relative error = 42.06165030061562 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y1[1] (closed_form) = 0.9358968236779348 y1[1] (numeric) = 0.9482794849140348 absolute error = 0.01238266123609999 relative error = 1.323079737298176 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3522742332750901 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1536049024800289 relative error = 43.60378590621449 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y1[1] (closed_form) = 0.9323273456060344 y1[1] (numeric) = 0.9462927916060844 absolute error = 0.01396544600005001 relative error = 1.497912301496654 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3616154319649622 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1629461011699009 relative error = 45.06060493173013 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y1[1] (closed_form) = 0.9286646355765101 y1[1] (numeric) = 0.9443060982981339 absolute error = 0.01564146272162381 relative error = 1.684296151959493 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3709204694129828 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1722511386179216 relative error = 46.43883334088451 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y1[1] (closed_form) = 0.924909059857313 y1[1] (numeric) = 0.9423194049901835 absolute error = 0.01741034513287054 relative error = 1.882384537951922 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3801884151231616 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1815190843281004 relative error = 47.74450696223805 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y1[1] (closed_form) = 0.921060994002885 y1[1] (numeric) = 0.9403327116822331 absolute error = 0.0192717176793481 relative error = 2.092338922701979 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3894183423086507 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1907490115135895 relative error = 48.98305775294039 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y1[1] (closed_form) = 0.917120822816605 y1[1] (numeric) = 0.9383460183742827 absolute error = 0.02122519555767766 relative error = 2.314329260619353 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.3986093279844231 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1999399971893618 relative error = 50.15938743841317 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y1[1] (closed_form) = 0.9130889403123081 y1[1] (numeric) = 0.9363593250663322 absolute error = 0.0232703847540241 relative error = 2.548534291310638 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4077604530595704 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2090911222645092 relative error = 51.27793063197394 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y1[1] (closed_form) = 0.9089657496748851 y1[1] (numeric) = 0.9343726317583818 absolute error = 0.02540688208349673 relative error = 2.79514185133864 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.416870802429211 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2182014716341498 relative error = 52.3427091469671 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y1[1] (closed_form) = 0.9047516632199634 y1[1] (numeric) = 0.9323859384504314 absolute error = 0.02763427523046802 relative error = 3.054349204744105 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4259394650659998 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2272701342709386 relative error = 53.3573789025919 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y1[1] (closed_form) = 0.9004471023526768 y1[1] (numeric) = 0.930399245142481 absolute error = 0.02995214278980418 relative error = 3.326363393423734 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4349655341112304 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2362962033161692 relative error = 54.32527057551714 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y1[1] (closed_form) = 0.8960524975255252 y1[1] (numeric) = 0.9284125518345305 absolute error = 0.03236005430900535 relative error = 3.611401608540635 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.44394810696552 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2452787761704588 relative error = 55.24942494900846 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y1[1] (closed_form) = 0.8915682881953289 y1[1] (numeric) = 0.9264258585265801 absolute error = 0.03485757033125125 relative error = 3.909691584231684 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4528862853790685 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2542169545840073 relative error = 56.13262374929861 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y1[1] (closed_form) = 0.886994922779284 y1[1] (numeric) = 0.9244391652186297 absolute error = 0.03744424243934563 relative error = 4.22147201497151 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4617791755414831 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2631098447464219 relative error = 56.97741662730867 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y1[1] (closed_form) = 0.8823328586101213 y1[1] (numeric) = 0.9224524719106793 absolute error = 0.04011961330055791 relative error = 4.546992998056946 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4706258881711582 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.271956557376097 relative error = 57.7861448363825 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000002 y1[1] (closed_form) = 0.8775825618903726 y1[1] (numeric) = 0.9204657786027288 absolute error = 0.04288321671235618 relative error = 4.886516502787249 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4794255386042032 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.280756207809142 relative error = 58.56096206859026 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000002 y1[1] (closed_form) = 0.8727445076457512 y1[1] (numeric) = 0.9184790852947784 absolute error = 0.04573457764902722 relative error = 5.240316868037052 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4881772468829077 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2895079160878465 relative error = 59.30385283959921 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000002 y1[1] (closed_form) = 0.8678191796776498 y1[1] (numeric) = 0.916492391986828 absolute error = 0.0486732123091782 relative error = 5.608681330050553 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.4968801378437369 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2982108070486757 relative error = 60.01664875211002 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000002 y1[1] (closed_form) = 0.8628070705147609 y1[1] (numeric) = 0.9145056986788775 absolute error = 0.05169862816411663 relative error = 5.991910582428656 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5055333412048472 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3068640104097859 relative error = 60.70104291804595 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000003 y1[1] (closed_form) = 0.8577086813638241 y1[1] (numeric) = 0.9125190053709271 absolute error = 0.05481032400710306 relative error = 6.390319370435933 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5141359916531133 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3154666608580521 relative error = 61.35860277817253 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000003 y1[1] (closed_form) = 0.8525245220595056 y1[1] (numeric) = 0.9105323120629767 absolute error = 0.05800779000347112 relative error = 6.804237121923188 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5226872289306594 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3240178981355982 relative error = 61.99078152310911 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000003 y1[1] (closed_form) = 0.847255111013416 y1[1] (numeric) = 0.9085456187550263 absolute error = 0.06129050774161027 relative error = 7.234008617345449 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5311861979208836 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3325168671258224 relative error = 62.59892829055555 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000003 y1[1] (closed_form) = 0.8419009751622686 y1[1] (numeric) = 0.9065589254470758 absolute error = 0.06465795028480725 relative error = 7.679994701555612 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5396320487339695 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3409627179389083 relative error = 63.18429728902142 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000003 y1[1] (closed_form) = 0.8364626499151868 y1[1] (numeric) = 0.9045722321391254 absolute error = 0.06810958222393859 relative error = 8.14257304027198 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5480239367918738 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3493546059968126 relative error = 63.7480559776149 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000003 y1[1] (closed_form) = 0.8309406791001633 y1[1] (numeric) = 0.902585538831175 absolute error = 0.07164485973101165 relative error = 8.622138924357008 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.556361022912784 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3576916921177228 relative error = 64.29129241388196 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000003 y1[1] (closed_form) = 0.8253356149096781 y1[1] (numeric) = 0.9005988455232246 absolute error = 0.07526323061354645 relative error = 9.119106125304311 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5646424733950356 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3659731425999744 relative error = 64.81502186675425 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000003 y1[1] (closed_form) = 0.8196480178454794 y1[1] (numeric) = 0.8986121522152741 absolute error = 0.07896413436979477 relative error = 9.633907805616282 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.001 y2[1] (closed_form) = 0.5728674601004815 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3741981293054203 relative error = 65.32019277893451 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000003 y1[1] (closed_form) = 0.8138784566625338 y1[1] (numeric) = 0.8966254589073237 absolute error = 0.08274700224478992 relative error = 10.16699748806597 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.5810351605373053 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3823658297422441 relative error = 65.80769215216785 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000003 y1[1] (closed_form) = 0.8080275083121516 y1[1] (numeric) = 0.8946387655993733 absolute error = 0.08661125728722163 relative error = 10.71885008817826 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.5891447579422698 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3904754271472086 relative error = 66.27835041951968 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000003 y1[1] (closed_form) = 0.8020957578842924 y1[1] (numeric) = 0.8926520722914228 absolute error = 0.09055631440713041 relative error = 11.28996301463967 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.5971954413623923 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3985261105673311 relative error = 66.73294586076655 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000004 y1[1] (closed_form) = 0.7960837985490556 y1[1] (numeric) = 0.8906653789834724 absolute error = 0.09458158043441678 relative error = 11.88085734275731 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6051864057360399 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4065170749409787 relative error = 67.17220861009996 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000004 y1[1] (closed_form) = 0.7899922314973649 y1[1] (numeric) = 0.888678685675522 absolute error = 0.09868645417815713 relative error = 12.4920790665378 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6131168519734341 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4144475211783729 relative error = 67.59682429938015 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000004 y1[1] (closed_form) = 0.783821665880849 y1[1] (numeric) = 0.8866919923675716 absolute error = 0.1028703264867226 relative error = 13.12420043545469 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6209859870365599 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4223166562414987 relative error = 68.00743737501362 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000004 y1[1] (closed_form) = 0.7775727187509277 y1[1] (numeric) = 0.8847052990596211 absolute error = 0.1071325803086934 relative error = 13.7778213825182 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6287930240184688 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4301236932234076 relative error = 68.40465412204924 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000004 y1[1] (closed_form) = 0.7712460149971063 y1[1] (numeric) = 0.8827186057516707 absolute error = 0.1114725907545644 relative error = 14.45357105086405 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6365371822219682 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.437867851426907 relative error = 68.78904542519201 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000004 y1[1] (closed_form) = 0.7648421872844882 y1[1] (numeric) = 0.8807319124437203 absolute error = 0.1158897251592321 relative error = 15.15210942674194 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6442176872376913 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4455483564426301 relative error = 69.16114929304014 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000004 y1[1] (closed_form) = 0.7583618759905079 y1[1] (numeric) = 0.8787452191357699 absolute error = 0.120383343145262 relative error = 15.87412908751874 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6518337710215369 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4531644402264757 relative error = 69.52147316888602 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000004 y1[1] (closed_form) = 0.7518057291408947 y1[1] (numeric) = 0.8767585258278194 absolute error = 0.1249527966869247 relative error = 16.6203570741222 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6593846719714734 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4607153411764122 relative error = 69.87049604882897 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000004 y1[1] (closed_form) = 0.7451744023448701 y1[1] (numeric) = 0.874771832519869 absolute error = 0.1295974301749989 relative error = 17.39155689824953 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6668696350036982 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.468200304208637 relative error = 70.2086704256733 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000004 y1[1] (closed_form) = 0.7384685587295876 y1[1] (numeric) = 0.8727851392119186 absolute error = 0.134316580482331 relative error = 18.18853069566026 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6742879116281454 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4756185808330842 relative error = 70.53642407508814 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000004 y1[1] (closed_form) = 0.7316888688738206 y1[1] (numeric) = 0.8707984459039682 absolute error = 0.1391095770301476 relative error = 19.01212153797805 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6816387600233345 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4829694292282732 relative error = 70.85416169874786 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000005 y1[1] (closed_form) = 0.7248360107409049 y1[1] (numeric) = 0.8688117525960177 absolute error = 0.1439757418551129 relative error = 19.86321591665201 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.6889214451105516 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4902521143154904 relative error = 71.16226643762256 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000005 y1[1] (closed_form) = 0.7179106696109431 y1[1] (numeric) = 0.8668250592880673 absolute error = 0.1489143896771242 relative error = 20.7427464140943 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.696135238627357 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4974659078322958 relative error = 71.46110126721952 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000005 y1[1] (closed_form) = 0.7109135380122771 y1[1] (numeric) = 0.8648383659801169 absolute error = 0.1539248279678398 relative error = 21.65169457852997 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.7032794192004105 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.5046100884053493 relative error = 71.75101028536608 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000005 y1[1] (closed_form) = 0.7038453156522357 y1[1] (numeric) = 0.8628516726721664 absolute error = 0.1590063570199307 relative error = 22.59109402079113 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 y2[1] (closed_form) = 0.7103532724176082 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.5116839416225469 relative error = 72.03231990205207 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 0.001 Finished! diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 1 ) = y1 ; Iterations = 600 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %