##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0)); ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 5.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.530159160995152 y[1] (numeric) = 1.530159160995152 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = 1.505836332328024 y[1] (numeric) = 1.505836332328024 absolute error = 2.220446049250313e-16 relative error = 1.474560017965234e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.476290817177127 y[1] (numeric) = 1.476290817177127 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.441752966693597 y[1] (numeric) = 1.441752966693597 absolute error = 2.220446049250313e-16 relative error = 1.54010159891851e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.402448017104221 y[1] (numeric) = 1.402448017104221 absolute error = 2.220446049250313e-16 relative error = 1.583264422046171e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.358596166945045 y[1] (numeric) = 1.358596166945045 absolute error = 2.220446049250313e-16 relative error = 1.634367962514743e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.310412653406727 y[1] (numeric) = 1.310412653406727 absolute error = 4.440892098500626e-16 relative error = 3.388926447676981e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.258107827799914 y[1] (numeric) = 1.258107827799914 absolute error = 4.440892098500626e-16 relative error = 3.529818351314553e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 0.9000000000000007 y[1] (analytic) = 1.201887230148848 y[1] (numeric) = 1.201887230148848 absolute error = 2.220446049250313e-16 relative error = 1.847466212762175e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.141951662921328 y[1] (numeric) = 1.141951662921328 absolute error = 4.440892098500626e-16 relative error = 3.888861711659482e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.075235629838208 y[1] (numeric) = 1.075235629838207 absolute error = 8.881784197001252e-16 relative error = 8.260314251619161e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 1.204999999999996 y[1] (analytic) = 1.008292526481616 y[1] (numeric) = 1.008292526481613 absolute error = 2.664535259100376e-15 relative error = 2.6426212523841e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.9382183938876646 y[1] (numeric) = 0.9382183938876605 absolute error = 4.107825191113079e-15 relative error = 4.378325151025466e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.8651955838829877 y[1] (numeric) = 0.8651955838829825 absolute error = 5.218048215738236e-15 relative error = 6.031062008337695e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.789402070168547 y[1] (numeric) = 0.7894020701685398 absolute error = 7.216449660063518e-15 relative error = 9.14166548679397e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 1.604999999999988 y[1] (analytic) = 0.7110115169945345 y[1] (numeric) = 0.711011516994526 absolute error = 8.43769498715119e-15 relative error = 1.186717062308296e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.6301933470272335 y[1] (numeric) = 0.6301933470272231 absolute error = 1.043609643147647e-14 relative error = 1.656015012012731e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.5471128084154596 y[1] (numeric) = 0.5471128084154476 absolute error = 1.199040866595169e-14 relative error = 2.191578862991372e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.4619310410641764 y[1] (numeric) = 0.4619310410641623 absolute error = 1.409983241273949e-14 relative error = 3.052367379394317e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.3748051421227862 y[1] (numeric) = 0.3748051421227708 absolute error = 1.532107773982716e-14 relative error = 4.087744808689944e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.104999999999977 y[1] (analytic) = 0.2858882306955695 y[1] (numeric) = 0.2858882306955514 absolute error = 1.809663530139005e-14 relative error = 6.329968623528405e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.1953295117816468 y[1] (numeric) = 0.1953295117816267 absolute error = 2.017830347256222e-14 relative error = 1.0330391597517e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.1032743394518305 y[1] (numeric) = 0.103274339451809 absolute error = 2.145505995088115e-14 relative error = 2.077482176575749e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.009864279269626705 y[1] (numeric) = 0.009864279269602936 absolute error = 2.376918106783421e-14 relative error = 2.40962166805459e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.504999999999969 y[1] (analytic) = -0.08476283003639005 y[1] (numeric) = -0.08476283003641558 absolute error = 2.552125177857079e-14 relative error = 3.010901331115785e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -0.1804728156416472 y[1] (numeric) = -0.1804728156416756 absolute error = 2.833844270355712e-14 relative error = 1.570233312025611e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -0.2771351104290078 y[1] (numeric) = -0.2771351104290372 absolute error = 2.942091015256665e-14 relative error = 1.061608906465254e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -0.3746226935194845 y[1] (numeric) = -0.3746226935195162 absolute error = 3.169686735304822e-14 relative error = 8.46101101224388e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -0.4728120315232768 y[1] (numeric) = -0.4728120315233115 absolute error = 3.469446951953614e-14 relative error = 7.33789903944695e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -0.571583020504164 y[1] (numeric) = -0.5715830205042002 absolute error = 3.61932706027801e-14 relative error = 6.332110875311846e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -0.6708189286503744 y[1] (numeric) = -0.6708189286504125 absolute error = 3.808064974464287e-14 relative error = 5.676740491097592e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.7704063396451247 y[1] (numeric) = -0.7704063396451646 absolute error = 3.985700658404312e-14 relative error = 5.173504491461299e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.8702350967300307 y[1] (numeric) = -0.8702350967300729 absolute error = 4.218847493575595e-14 relative error = 4.847939952580871e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.9701982474546875 y[1] (numeric) = -0.9701982474547329 absolute error = 4.54081217071689e-14 relative error = 4.680293107753698e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.504999999999947 y[1] (analytic) = -1.070191989105752 y[1] (numeric) = -1.070191989105798 absolute error = 4.618527782440651e-14 relative error = 4.315606759773894e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -1.1701156148089 y[1] (numeric) = -1.17011561480895 absolute error = 4.907185768843192e-14 relative error = 4.193761459755084e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -1.269871460297152 y[1] (numeric) = -1.269871460297203 absolute error = 5.10702591327572e-14 relative error = 4.021687291153601e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -1.369364851338979 y[1] (numeric) = -1.369364851339034 absolute error = 5.46229728115577e-14 relative error = 3.988927622769548e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -1.468504051819839 y[1] (numeric) = -1.468504051819896 absolute error = 5.662137425588298e-14 relative error = 3.855717945463965e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -1.567200212470649 y[1] (numeric) = -1.567200212470708 absolute error = 5.88418203051333e-14 relative error = 3.754582205701131e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -1.665367320236917 y[1] (numeric) = -1.665367320236977 absolute error = 6.017408793468348e-14 relative error = 3.613262203687476e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -1.762922148282199 y[1] (numeric) = -1.762922148282261 absolute error = 6.23945339839338e-14 relative error = 3.539267689428678e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -1.859784206619656 y[1] (numeric) = -1.85978420661972 absolute error = 6.394884621840902e-14 relative error = 3.438508940488448e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -1.955875693365499 y[1] (numeric) = -1.955875693365565 absolute error = 6.59472476627343e-14 relative error = 3.371750458704156e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -2.051121446608203 y[1] (numeric) = -2.051121446608271 absolute error = 6.794564910705958e-14 relative error = 3.312609754016106e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -2.145448896887376 y[1] (numeric) = -2.145448896887446 absolute error = 7.061018436615996e-14 relative error = 3.291161326126269e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -2.238788020276255 y[1] (numeric) = -2.238788020276326 absolute error = 7.105427357601002e-14 relative error = 3.173782999215901e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -2.33107129206182 y[1] (numeric) = -2.331071292061894 absolute error = 7.460698725481052e-14 relative error = 3.200545067363472e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.904999999999918 y[1] (analytic) = -2.422233641016603 y[1] (numeric) = -2.422233641016678 absolute error = 7.505107646466058e-14 relative error = 3.098424330080806e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 5.004999999999916 y[1] (analytic) = -2.512212404256268 y[1] (numeric) = -2.512212404256345 absolute error = 7.682743330406083e-14 relative error = 3.058158345763177e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0)); Iterations = 981 Total Elapsed Time = 46 Seconds Elapsed Time(since restart) = 46 Seconds Time to Timeout = 9 Minutes 14 Seconds Percent Done = 100.2 %