##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.2; x_end=0.6; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.01; glob_max_minutes=10; glob_max_h=0.0001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(cos(x)); } double exact_soln_y2 (double x) { return(sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000 step_error = 2.5e-16 est_needed_step_err = 2.5e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y1[1] (analytic) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412416 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 y2[1] (analytic) = 0.1986693307950612 y2[1] (numeric) = 0.1986693307950612 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100999999999989 y1[1] (analytic) = 0.978010063844044 y1[1] (numeric) = 0.9780600176002083 absolute error = 4.995375616434483e-05 relative error = 0.00510769346973822 % Correct digits = 5 h = 0.0001 y2[1] (analytic) = 0.2085577018951084 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.0098883711000472 relative error = 4.741311881649155 % Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200999999999978 y1[1] (analytic) = 0.975875621488847 y1[1] (numeric) = 0.9760733242922546 absolute error = 0.0001977028034075845 relative error = 0.02025901652363841 % Correct digits = 4 h = 0.0001 y2[1] (analytic) = 0.2183272117344895 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.01965788093942825 relative error = 9.003862039576838 % Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300999999999967 y1[1] (analytic) = 0.9736435923847281 y1[1] (numeric) = 0.9740866309843008 absolute error = 0.0004430385995727315 relative error = 0.04550315978433185 % Correct digits = 4 h = 0.0001 y2[1] (analytic) = 0.2280748890346358 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.02940555823957461 relative error = 12.89293984271501 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400999999999956 y1[1] (analytic) = 0.9713141997327377 y1[1] (numeric) = 0.9720999376763471 absolute error = 0.0007857379436093659 relative error = 0.08089431245065355 % Correct digits = 4 h = 0.0001 y2[1] (analytic) = 0.2377997590359405 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.03913042824087928 relative error = 16.45520096383495 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500999999999945 y1[1] (analytic) = 0.9688876764701998 y1[1] (numeric) = 0.9701132443683933 absolute error = 0.001225567898193503 relative error = 0.1264922578702236 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.2475008492595074 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.04883151846444617 relative error = 19.7298387502686 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600999999999934 y1[1] (analytic) = 0.9663642652474187 y1[1] (numeric) = 0.9681265510604395 absolute error = 0.001762285813020847 relative error = 0.1823624772144951 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.2571771896043983 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.05850785880933712 relative error = 22.75001873196319 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700999999999923 y1[1] (analytic) = 0.9637442184034136 y1[1] (numeric) = 0.9661398577524858 absolute error = 0.002395639349072165 relative error = 0.2485762615562976 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.2668278124446425 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.06815848164958127 relative error = 25.54399446786372 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800999999999912 y1[1] (analytic) = 0.9610277979406858 y1[1] (numeric) = 0.964153164444532 absolute error = 0.003125366503846205 relative error = 0.3252108326672046 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.2764517527259979 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.07778242193093671 relative error = 28.13598436759773 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900999999999901 y1[1] (analytic) = 0.9582152754990179 y1[1] (numeric) = 0.9621664711365783 absolute error = 0.003951195637560412 relative error = 0.4123494728783899 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.2860480480624565 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.08737871726739527 relative error = 30.54686716418941 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.300099999999989 y1[1] (analytic) = 0.95530693232831 y1[1] (numeric) = 0.9601797778286245 absolute error = 0.004872845500314527 relative error = 0.510081664375474 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.2956157388324814 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.09694640803742016 relative error = 32.79473833846088 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100999999999879 y1[1] (analytic) = 0.9523030592604558 y1[1] (numeric) = 0.9581930845206708 absolute error = 0.005890025260214982 relative error = 0.6185032383272071 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3051538682749687 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1064845374799074 relative error = 34.89535888300001 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200999999999868 y1[1] (analytic) = 0.9492039566802588 y1[1] (numeric) = 0.956206391212717 absolute error = 0.00700243453245819 relative error = 0.7377165342787307 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3146614825849224 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1159921517898612 relative error = 36.86251994905562 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300999999999857 y1[1] (analytic) = 0.9460099344953944 y1[1] (numeric) = 0.9542196979047632 absolute error = 0.008209763409368853 relative error = 0.8678305702728137 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3241376310088348 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1254683002137736 relative error = 38.70834121396839 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400999999999846 y1[1] (analytic) = 0.9427213121054195 y1[1] (numeric) = 0.9522330045968095 absolute error = 0.009511692491389945 relative error = 1.008961224197539 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3335813659397601 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1349120351446989 relative error = 40.44351661089548 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500999999999835 y1[1] (analytic) = 0.9393384183698327 y1[1] (numeric) = 0.9502463112888557 absolute error = 0.01090789291902305 relative error = 1.161231426896503 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.342991743012075 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1443224122170138 relative error = 42.07751794536141 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600999999999824 y1[1] (analytic) = 0.9358615915751881 y1[1] (numeric) = 0.948259617980902 absolute error = 0.01239802640571386 relative error = 1.324771367617108 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3523678211959141 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1536984904008529 relative error = 43.61876458503218 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700999999999813 y1[1] (analytic) = 0.9322911794012683 y1[1] (numeric) = 0.9462729246729482 absolute error = 0.01398174527167995 relative error = 1.499718712415496 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3617086628912726 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1630393320962114 relative error = 45.07476563955561 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800999999999802 y1[1] (analytic) = 0.928627538886315 y1[1] (numeric) = 0.9442862313649945 absolute error = 0.01565869247867946 relative error = 1.686218836182548 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3710133340217648 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1723440032267036 relative error = 46.45223969675261 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900999999999791 y1[1] (analytic) = 0.9248710363913267 y1[1] (numeric) = 0.9422995380570407 absolute error = 0.01742850166571397 relative error = 1.88442506900386 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3802809041280316 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1816115733329703 relative error = 47.75721614247189 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.400099999999978 y1[1] (analytic) = 0.9210220475634228 y1[1] (numeric) = 0.9403128447490869 absolute error = 0.01929079718566418 relative error = 2.094498957619773 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3895104464607853 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.190841115665724 relative error = 48.99512128615974 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100999999999769 y1[1] (analytic) = 0.9170809572982782 y1[1] (numeric) = 0.9383261514411332 absolute error = 0.02124519414285497 relative error = 2.316610542807839 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.3987010380734838 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2000317072784226 relative error = 50.17085188565653 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200999999999758 y1[1] (analytic) = 0.9130481597016354 y1[1] (numeric) = 0.9363394581331794 absolute error = 0.02329129843154398 relative error = 2.550938653570594 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4078517599146249 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2091824291195636 relative error = 51.28883817084706 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300999999999747 y1[1] (analytic) = 0.9089240580498935 y1[1] (numeric) = 0.9343527648252257 absolute error = 0.02542870677533215 relative error = 2.797671219077392 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4169616969196497 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2182923661245885 relative error = 52.35309807525423 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400999999999736 y1[1] (analytic) = 0.9047090647497807 y1[1] (numeric) = 0.9323660715172719 absolute error = 0.02765700676749117 relative error = 3.057005599379109 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4260299381024495 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2273606073073883 relative error = 53.36728407399242 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500999999999725 y1[1] (analytic) = 0.9004036012971147 y1[1] (numeric) = 0.9303793782093182 absolute error = 0.02997577691220343 relative error = 3.329148935990544 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4350555766464629 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2363862458514017 relative error = 54.33472377794507 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600999999999714 y1[1] (analytic) = 0.8960080982346529 y1[1] (numeric) = 0.9283926849013644 absolute error = 0.03238458666671151 relative error = 3.614318523517452 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4440377099953568 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2453683792002956 relative error = 55.25845523409743 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700999999999703 y1[1] (analytic) = 0.8915229951090385 y1[1] (numeric) = 0.9264059915934106 absolute error = 0.0348829964843721 relative error = 3.912742203593492 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4529754399432813 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.25430610914822 relative error = 56.14125772029995 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800999999999692 y1[1] (analytic) = 0.8869487404268467 y1[1] (numeric) = 0.9244192982854569 absolute error = 0.0374705578586102 relative error = 4.224658782488082 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4618678727246898 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2631985419296285 relative error = 56.9856786913854 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900999999999681 y1[1] (analytic) = 0.8822857916097335 y1[1] (numeric) = 0.9224326049775031 absolute error = 0.0401468133677696 relative error = 4.550318473849794 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4707141191037144 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2720447883086531 relative error = 57.79405742633192 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.500099999999967 y1[1] (analytic) = 0.8775346149486952 y1[1] (numeric) = 0.9204459116695494 absolute error = 0.04291129672085414 relative error = 4.889983368161829 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4795132944630892 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2808439636680279 relative error = 58.56854583823141 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100999999999659 y1[1] (analytic) = 0.8726956855574385 y1[1] (numeric) = 0.9184592183615956 absolute error = 0.04576353280415713 relative error = 5.24392793060796 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4882645188926106 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2895951880975494 relative error = 59.31112683640305 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200999999999648 y1[1] (analytic) = 0.8677694873248699 y1[1] (numeric) = 0.9164725250536419 absolute error = 0.04870303772877194 relative error = 5.612439529178652 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.4969669172771286 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2982975864820674 relative error = 60.02363057010588 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300999999999637 y1[1] (analytic) = 0.8627565128667077 y1[1] (numeric) = 0.9144858317456881 absolute error = 0.05172931887898036 relative error = 5.995818994990574 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.5056196193840566 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3069502885889954 relative error = 60.70774883358379 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400999999999626 y1[1] (analytic) = 0.8576572634762204 y1[1] (numeric) = 0.9124991384377343 absolute error = 0.05484187496151394 relative error = 6.394381216948033 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.5142217599503945 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3155524291553333 relative error = 61.36504787074234 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500999999999615 y1[1] (analytic) = 0.8524722490740974 y1[1] (numeric) = 0.9105124451297806 absolute error = 0.05804019605568322 relative error = 6.808455773043979 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.522772478769254 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3241031479741928 relative error = 61.99697978310147 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600999999999604 y1[1] (analytic) = 0.8472019881574581 y1[1] (numeric) = 0.9085257518218268 absolute error = 0.06132376366436876 relative error = 7.238387600782086 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.531270920775879 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3326015899808178 relative error = 62.60489271558089 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700999999999593 y1[1] (analytic) = 0.8418470077480024 y1[1] (numeric) = 0.9065390585138731 absolute error = 0.0646920507658707 relative error = 7.684537709402366 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.5397162361331507 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3410469053380895 relative error = 63.19003997018009 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800999999999582 y1[1] (analytic) = 0.8364078433393087 y1[1] (numeric) = 0.9045523652059193 absolute error = 0.06814452186661057 relative error = 8.147283936810972 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.548107580316571 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3494382495215098 relative error = 63.75358817692039 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900999999999571 y1[1] (analytic) = 0.8308850388432855 y1[1] (numeric) = 0.9025656718979655 absolute error = 0.07168063305468009 relative error = 8.627021754353658 % Correct digits = 3 h = 0.0001 y2[1] (analytic) = 0.5564441141987145 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3577747834036533 relative error = 64.29662463387771 % Correct digits = 2 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; Iterations = 4001 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 9 Minutes 59.0 Seconds Percent Done = 100 %