##############ECHO OF PROBLEM################# ##############temp/ln_c_exp_c_sqrt_cpostode.ode################# diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1); ! /* 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((ln(0.1) + exp(0.1) + sqrt(0.1)) * x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.08811864089015599 y[1] (numeric) = -0.08811864089015599 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) = -0.176237281780312 y[1] (numeric) = -0.1762372817803119 absolute error = 1.665334536937735e-16 relative error = 9.449388461481446e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -0.2643559226704681 y[1] (numeric) = -0.2643559226704676 absolute error = 4.440892098500626e-16 relative error = 1.679891282041146e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -0.3524745635606241 y[1] (numeric) = -0.3524745635606234 absolute error = 7.216449660063518e-16 relative error = 2.047367499987646e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -0.4405932044507802 y[1] (numeric) = -0.4405932044507792 absolute error = 1.054711873393899e-15 relative error = 2.393845076908632e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -0.5287118453409363 y[1] (numeric) = -0.528711845340935 absolute error = 1.332267629550188e-15 relative error = 2.519836923061718e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -0.6168304862310923 y[1] (numeric) = -0.6168304862310907 absolute error = 1.554312234475219e-15 relative error = 2.519836923061719e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.7049491271212484 y[1] (numeric) = -0.7049491271212465 absolute error = 1.887379141862766e-15 relative error = 2.677326730753076e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.7930677680114044 y[1] (numeric) = -0.7930677680114022 absolute error = 2.220446049250313e-15 relative error = 2.799818803401909e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.8811864089015604 y[1] (numeric) = -0.881186408901558 absolute error = 2.442490654175344e-15 relative error = 2.77182061536789e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.9737109818362222 y[1] (numeric) = -0.9737109818362215 absolute error = 6.661338147750939e-16 relative error = 6.841186216457168e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -1.061829622726376 y[1] (numeric) = -1.061829622726377 absolute error = 8.881784197001252e-16 relative error = 8.364603893980839e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -1.14994826361653 y[1] (numeric) = -1.149948263616533 absolute error = 2.664535259100376e-15 relative error = 2.31709142350504e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -1.238066904506685 y[1] (numeric) = -1.238066904506689 absolute error = 4.218847493575595e-15 relative error = 3.407608650403769e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -1.326185545396839 y[1] (numeric) = -1.326185545396845 absolute error = 5.995204332975845e-15 relative error = 4.520637669280193e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -1.414304186286993 y[1] (numeric) = -1.414304186287 absolute error = 7.549516567451064e-15 relative error = 5.337972298074713e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -1.502422827177147 y[1] (numeric) = -1.502422827177156 absolute error = 9.325873406851315e-15 relative error = 6.20722291897907e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -1.590541468067301 y[1] (numeric) = -1.590541468067312 absolute error = 1.088018564132653e-14 relative error = 6.840554527979247e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -1.678660108957455 y[1] (numeric) = -1.678660108957468 absolute error = 1.243449787580175e-14 relative error = 7.407394629472845e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -1.766778749847609 y[1] (numeric) = -1.766778749847623 absolute error = 1.398881011027697e-14 relative error = 7.917692077450872e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -1.854897390737763 y[1] (numeric) = -1.854897390737779 absolute error = 1.554312234475219e-14 relative error = 8.379505207331225e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -1.943016031627917 y[1] (numeric) = -1.943016031627935 absolute error = 1.731947918415244e-14 relative error = 8.913708843483736e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -2.031134672518072 y[1] (numeric) = -2.031134672518092 absolute error = 2.042810365310288e-14 relative error = 1.005748359746989e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -2.119253313408226 y[1] (numeric) = -2.119253313408252 absolute error = 2.664535259100376e-14 relative error = 1.257299088429979e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -2.20737195429838 y[1] (numeric) = -2.207371954298412 absolute error = 3.286260152890463e-14 relative error = 1.488765926599358e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -2.295490595188534 y[1] (numeric) = -2.295490595188573 absolute error = 3.863576125695545e-14 relative error = 1.683115641507658e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -2.383609236078688 y[1] (numeric) = -2.383609236078733 absolute error = 4.485301019485632e-14 relative error = 1.881726648645006e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -2.471727876968842 y[1] (numeric) = -2.471727876968893 absolute error = 5.10702591327572e-14 relative error = 2.06617644315224e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -2.559846517858996 y[1] (numeric) = -2.559846517859053 absolute error = 5.684341886080801e-14 relative error = 2.220579181768706e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -2.64796515874915 y[1] (numeric) = -2.647965158749213 absolute error = 6.306066779870889e-14 relative error = 2.381476493010111e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -2.736083799639304 y[1] (numeric) = -2.736083799639374 absolute error = 6.927791673660977e-14 relative error = 2.532010048293938e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -2.824202440529458 y[1] (numeric) = -2.824202440529534 absolute error = 7.549516567451064e-14 relative error = 2.67314993398127e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -2.912321081419613 y[1] (numeric) = -2.912321081419694 absolute error = 8.126832540256146e-14 relative error = 2.7905001931637e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -3.000439722309767 y[1] (numeric) = -3.000439722309854 absolute error = 8.748557434046234e-14 relative error = 2.91575843667058e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -3.088558363199921 y[1] (numeric) = -3.088558363200014 absolute error = 9.370282327836321e-14 relative error = 3.033869276838978e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -3.176677004090075 y[1] (numeric) = -3.176677004090175 absolute error = 9.947598300641403e-14 relative error = 3.131447826717525e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -3.264795644980229 y[1] (numeric) = -3.264795644980335 absolute error = 1.056932319443149e-13 relative error = 3.237361337051004e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -3.352914285870383 y[1] (numeric) = -3.352914285870495 absolute error = 1.119104808822158e-13 relative error = 3.337707777196128e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -3.441032926760537 y[1] (numeric) = -3.441032926760655 absolute error = 1.181277298201167e-13 relative error = 3.432914835003473e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -3.529151567650691 y[1] (numeric) = -3.529151567650815 absolute error = 1.239008895481675e-13 relative error = 3.510784027636609e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -3.617270208540845 y[1] (numeric) = -3.617270208540976 absolute error = 1.301181384860683e-13 relative error = 3.597136265320807e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -3.705388849430999 y[1] (numeric) = -3.705388849431136 absolute error = 1.363353874239692e-13 relative error = 3.679381381117529e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -3.793507490321154 y[1] (numeric) = -3.793507490321296 absolute error = 1.4210854715202e-13 relative error = 3.746099026154534e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -3.881626131211308 y[1] (numeric) = -3.881626131211456 absolute error = 1.483257960899209e-13 relative error = 3.821228296493204e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -3.969744772101462 y[1] (numeric) = -3.969744772101616 absolute error = 1.545430450278218e-13 relative error = 3.893022194119835e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -4.057863412991616 y[1] (numeric) = -4.057863412991771 absolute error = 1.545430450278218e-13 relative error = 3.808483167103118e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -4.14598205388177 y[1] (numeric) = -4.145982053881922 absolute error = 1.518785097687214e-13 relative error = 3.663269830763539e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -4.234100694771924 y[1] (numeric) = -4.234100694772073 absolute error = 1.49213974509621e-13 relative error = 3.524100754001049e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -4.322219335662078 y[1] (numeric) = -4.322219335662225 absolute error = 1.465494392505207e-13 relative error = 3.390606257330812e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -4.410337976552232 y[1] (numeric) = -4.410337976552376 absolute error = 1.438849039914203e-13 relative error = 3.262446206081963e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1); Iterations = 981 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 18 Seconds Time to Timeout = 9 Minutes 42 Seconds Percent Done = 100.2 %