##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb 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 def exact_soln_y1 (x) return(cos(x)) end def exact_soln_y2 (x) return(sin(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.39999999999999997 estimated_steps 400000.0 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 0.0 estimated_step_error 0.0 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 0.0 estimated_step_error 0.0 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 0.0 estimated_step_error 0.0 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 0.0 estimated_step_error 0.0 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 0.0 estimated_step_error 0.0 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 0.0 relative error 0.0% Correct digits 16 h 0.0001 y2[1] (analytic) 0.19866933079506122 y2[1] (numeric) 0.19866933079506122 absolute error 0.0 relative error 0.0% 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) 0.20855770189510842 y2[1] (numeric) 0.19866933079506122 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 0.020259016523638408% Correct digits 4 h 0.0001 y2[1] (analytic) 0.21832721173448946 y2[1] (numeric) 0.19866933079506122 absolute error 0.019657880939428246 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) 0.22807488903463582 y2[1] (numeric) 0.19866933079506122 absolute error 0.02940555823957461 relative error 12.892939842715009% 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) 0.19866933079506122 absolute error 0.039130428240879284 relative error 16.455200963834955% 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 0.0012255678981935025 relative error 0.12649225787022356% Correct digits 3 h 0.0001 y2[1] (analytic) 0.24750084925950738 y2[1] (numeric) 0.19866933079506122 absolute error 0.048831518464446166 relative error 19.729838750268602% 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 0.0017622858130208474 relative error 0.18236247721449514% Correct digits 3 h 0.0001 y2[1] (analytic) 0.25717718960439834 y2[1] (numeric) 0.19866933079506122 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 0.24857626155629756% Correct digits 3 h 0.0001 y2[1] (analytic) 0.2668278124446425 y2[1] (numeric) 0.19866933079506122 absolute error 0.06815848164958127 relative error 25.543994467863723% 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 0.0031253665038462053 relative error 0.32521083266720463% Correct digits 3 h 0.0001 y2[1] (analytic) 0.2764517527259979 y2[1] (numeric) 0.19866933079506122 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) 0.19866933079506122 absolute error 0.08737871726739527 relative error 30.546867164189415% 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) 0.19866933079506122 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) 0.30515386827496865 y2[1] (numeric) 0.19866933079506122 absolute error 0.10648453747990744 relative error 34.895358883000014% 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 0.0070024345324581905 relative error 0.7377165342787307% Correct digits 3 h 0.0001 y2[1] (analytic) 0.31466148258492244 y2[1] (numeric) 0.19866933079506122 absolute error 0.11599215178986122 relative error 36.862519949055624% 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) 0.19866933079506122 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 1.0089612241975392% Correct digits 3 h 0.0001 y2[1] (analytic) 0.3335813659397601 y2[1] (numeric) 0.19866933079506122 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 0.010907892919023054 relative error 1.1612314268965034% Correct digits 3 h 0.0001 y2[1] (analytic) 0.34299174301207497 y2[1] (numeric) 0.19866933079506122 absolute error 0.14432241221701375 relative error 42.077517945361414% 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 0.012398026405713858 relative error 1.3247713676171085% Correct digits 3 h 0.0001 y2[1] (analytic) 0.35236782119591414 y2[1] (numeric) 0.19866933079506122 absolute error 0.15369849040085293 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 0.013981745271679946 relative error 1.4997187124154965% Correct digits 3 h 0.0001 y2[1] (analytic) 0.36170866289127257 y2[1] (numeric) 0.19866933079506122 absolute error 0.16303933209621135 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) 0.19866933079506122 absolute error 0.17234400322670357 relative error 46.452239696752606% 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 1.8844250690038595% Correct digits 3 h 0.0001 y2[1] (analytic) 0.38028090412803156 y2[1] (numeric) 0.19866933079506122 absolute error 0.18161157333297034 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 0.019290797185664177 relative error 2.0944989576197726% Correct digits 3 h 0.0001 y2[1] (analytic) 0.38951044646078525 y2[1] (numeric) 0.19866933079506122 absolute error 0.19084111566572404 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] 0.41009999999997687 y1[1] (analytic) 0.9170809572982782 y1[1] (numeric) 0.9383261514411332 absolute error 0.021245194142854973 relative error 2.3166105428078394% Correct digits 3 h 0.0001 y2[1] (analytic) 0.39870103807348384 y2[1] (numeric) 0.19866933079506122 absolute error 0.20003170727842262 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] 0.42009999999997577 y1[1] (analytic) 0.9130481597016354 y1[1] (numeric) 0.9363394581331794 absolute error 0.023291298431543983 relative error 2.5509386535705936% Correct digits 3 h 0.0001 y2[1] (analytic) 0.40785175991462486 y2[1] (numeric) 0.19866933079506122 absolute error 0.20918242911956364 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] 0.43009999999997467 y1[1] (analytic) 0.9089240580498935 y1[1] (numeric) 0.9343527648252257 absolute error 0.025428706775332155 relative error 2.7976712190773916% Correct digits 3 h 0.0001 y2[1] (analytic) 0.41696169691964974 y2[1] (numeric) 0.19866933079506122 absolute error 0.21829236612458852 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] 0.44009999999997357 y1[1] (analytic) 0.9047090647497807 y1[1] (numeric) 0.9323660715172719 absolute error 0.027657006767491166 relative error 3.0570055993791088% Correct digits 3 h 0.0001 y2[1] (analytic) 0.42602993810244955 y2[1] (numeric) 0.19866933079506122 absolute error 0.22736060730738833 relative error 53.367284073992415% 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] 0.45009999999997247 y1[1] (analytic) 0.9004036012971147 y1[1] (numeric) 0.9303793782093182 absolute error 0.029975776912203433 relative error 3.3291489359905437% Correct digits 3 h 0.0001 y2[1] (analytic) 0.43505557664646294 y2[1] (numeric) 0.19866933079506122 absolute error 0.23638624585140172 relative error 54.334723777945065% 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] 0.46009999999997137 y1[1] (analytic) 0.8960080982346529 y1[1] (numeric) 0.9283926849013644 absolute error 0.03238458666671151 relative error 3.6143185235174524% Correct digits 3 h 0.0001 y2[1] (analytic) 0.4440377099953568 y2[1] (numeric) 0.19866933079506122 absolute error 0.24536837920029558 relative error 55.258455234097426% 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] 0.47009999999997026 y1[1] (analytic) 0.8915229951090385 y1[1] (numeric) 0.9264059915934106 absolute error 0.0348829964843721 relative error 3.9127422035934925% Correct digits 3 h 0.0001 y2[1] (analytic) 0.45297543994328127 y2[1] (numeric) 0.19866933079506122 absolute error 0.25430610914822005 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] 0.48009999999996916 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) 0.46186787272468977 y2[1] (numeric) 0.19866933079506122 absolute error 0.26319854192962855 relative error 56.985678691385395% 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] 0.49009999999996806 y1[1] (analytic) 0.8822857916097335 y1[1] (numeric) 0.9224326049775031 absolute error 0.040146813367769596 relative error 4.550318473849794% Correct digits 3 h 0.0001 y2[1] (analytic) 0.47071411910371436 y2[1] (numeric) 0.19866933079506122 absolute error 0.27204478830865314 relative error 57.794057426331925% 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) 0.47951329446308916 y2[1] (numeric) 0.19866933079506122 absolute error 0.28084396366802794 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 0.045763532804157125 relative error 5.24392793060796% Correct digits 3 h 0.0001 y2[1] (analytic) 0.48826451889261063 y2[1] (numeric) 0.19866933079506122 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 0.048703037728771936 relative error 5.612439529178652% Correct digits 3 h 0.0001 y2[1] (analytic) 0.4969669172771286 y2[1] (numeric) 0.19866933079506122 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) 0.19866933079506122 absolute error 0.3069502885889954 relative error 60.707748833583786% 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) 0.19866933079506122 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 0.058040196055683224 relative error 6.8084557730439785% Correct digits 3 h 0.0001 y2[1] (analytic) 0.522772478769254 y2[1] (numeric) 0.19866933079506122 absolute error 0.3241031479741928 relative error 61.996979783101466% 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) 0.19866933079506122 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) 0.19866933079506122 absolute error 0.34104690533808946 relative error 63.190039970180095% 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) 0.19866933079506122 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) 0.19866933079506122 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 41 Seconds Elapsed Time(since restart) 41 Seconds Time to Timeout 9 Minutes 19.0 Seconds Percent Done 100.049999999989%