##############ECHO OF PROBLEM################# ##############temp/mult_sin_linpostode.ode################# diff ( y , x , 1 ) = sin(x) * (0.2 * x + 0.3); ! /* 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(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.2984346495596026 y[1] (numeric) = -0.2984346495596026 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) = -0.2934887703070099 y[1] (numeric) = -0.2934887498537524 absolute error = 2.045325747657145e-08 relative error = 6.96900854338512e-06 % Correct digits = 7 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -0.2848170947529503 y[1] (numeric) = -0.2848170383187479 absolute error = 5.643420231127294e-08 relative error = 1.981419070376511e-05 % Correct digits = 6 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -0.2721195092593662 y[1] (numeric) = -0.2721194000640351 absolute error = 1.091953311105343e-07 relative error = 4.012771131615431e-05 % Correct digits = 6 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -0.2551479170353084 y[1] (numeric) = -0.2551477372627617 absolute error = 1.79772546682333e-07 relative error = 7.045816747054036e-05 % Correct digits = 6 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -0.2337124635830577 y[1] (numeric) = -0.2337121946238681 absolute error = 2.689591896420929e-07 relative error = 0.0001150812350863389 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -0.2076870249576366 y[1] (numeric) = -0.2076866476744972 absolute error = 3.772831393689113e-07 relative error = 0.0001816594654605258 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.1770138681197914 y[1] (numeric) = -0.1770133631324306 absolute error = 5.049873607332334e-07 relative error = 0.000285281241575655 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.141707402844422 y[1] (numeric) = -0.1417067508301871 absolute error = 6.520142349086822e-07 relative error = 0.000460113037019327 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.1018569559724903 y[1] (numeric) = -0.1018561379785284 absolute error = 8.179939618851995e-07 relative error = 0.0008030810994451129 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.05530620149450838 y[1] (numeric) = -0.05530518958242379 absolute error = 1.011912084597499e-06 relative error = 0.001829653921717941 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.006744096164736128 y[1] (numeric) = -0.006742881927013208 absolute error = 1.214237722919724e-06 relative error = 0.01800445446298337 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.04561452832879519 y[1] (numeric) = 0.045615960737306 absolute error = 1.432408510811112e-06 relative error = 0.003140246240158691 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.1013704927095471 y[1] (numeric) = 0.101372157472626 absolute error = 1.664763078904063e-06 relative error = 0.001642256079068339 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.1600521736505866 y[1] (numeric) = 0.1600540829885671 absolute error = 1.909337980443571e-06 relative error = 0.001192947235200871 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.2211193620726124 y[1] (numeric) = 0.2211215259563432 absolute error = 2.163883730865734e-06 relative error = 0.0009786043657973047 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.2839681999299103 y[1] (numeric) = 0.2839706258152535 absolute error = 2.425885343104728e-06 relative error = 0.0008542806355442229 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.3479371507617143 y[1] (numeric) = 0.3479398433488878 absolute error = 2.692587173502847e-06 relative error = 0.0007738717086140861 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.4123139449826562 y[1] (numeric) = 0.4123169060044878 absolute error = 2.961021831560107e-06 relative error = 0.000718147389287224 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.4763434271656858 y[1] (numeric) = 0.4763466552085397 absolute error = 3.228042853853363e-06 relative error = 0.0006776713332774839 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.5392362196108827 y[1] (numeric) = 0.5392397099716637 absolute error = 3.490360780955548e-06 relative error = 0.0006472786237308431 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.6001781044629069 y[1] (numeric) = 0.6001818490451414 absolute error = 3.744582234510574e-06 relative error = 0.00062391183661416 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.6583400156973593 y[1] (numeric) = 0.6583440029488993 absolute error = 3.987251539938619e-06 relative error = 0.0006056523141336086 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.7128885225889898 y[1] (numeric) = 0.712892737483393 absolute error = 4.214894403165026e-06 relative error = 0.0005912417256849413 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.7629966779355801 y[1] (numeric) = 0.7630011019986923 absolute error = 4.424063112185017e-06 relative error = 0.0005798273098848985 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.807855097458042 y[1] (numeric) = 0.8078597088407482 absolute error = 4.611382706243283e-06 relative error = 0.0005708180490230536 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.8466831315303208 y[1] (numeric) = 0.8466879051278584 absolute error = 4.773597537588437e-06 relative error = 0.0005637997687470744 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.8787399867942708 y[1] (numeric) = 0.8787448944119007 absolute error = 4.907617629945626e-06 relative error = 0.0005584834767618912 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.9033356533474587 y[1] (numeric) = 0.9033406639116898 absolute error = 5.010564231078263e-06 relative error = 0.0005546735825726344 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.9198414930981563 y[1] (numeric) = 0.9198465729121174 absolute error = 5.079813961028634e-06 relative error = 0.0005522488384296627 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.9277003465829156 y[1] (numeric) = 0.9277054596238737 absolute error = 5.113040958182324e-06 relative error = 0.0005511522095486609 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.926436019037877 y[1] (numeric) = 0.9264411272943207 absolute error = 5.10825644373103e-06 relative error = 0.0005513879359997315 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0.9156620117835905 y[1] (numeric) = 0.9156670756287391 absolute error = 5.063845148534085e-06 relative error = 0.0005530255796754496 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 0.8950893719812986 y[1] (numeric) = 0.8950943505793656 absolute error = 4.978598067029161e-06 relative error = 0.0005562123987696259 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.864533542481839 y[1] (numeric) = 0.8645383942228917 absolute error = 4.851741052691594e-06 relative error = 0.0005611975492314126 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.8239201037314782 y[1] (numeric) = 0.8239247866902757 absolute error = 4.682958797519454e-06 relative error = 0.0005683753529390352 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.7732893114172029 y[1] (numeric) = 0.7732937838310013 absolute error = 4.472413798417563e-06 relative error = 0.0005783622936958737 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 0.7127993466037278 y[1] (numeric) = 0.7128035673636874 absolute error = 4.220759959649989e-06 relative error = 0.0005921385842678767 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 0.6427282093947658 y[1] (numeric) = 0.6427321385453105 absolute error = 3.929150544701443e-06 relative error = 0.0006113238048787968 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.563474202485123 y[1] (numeric) = 0.5634778017253776 absolute error = 3.599240254614777e-06 relative error = 0.000638758658114398 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0.4755549671869218 y[1] (numeric) = 0.4755582003681945 absolute error = 3.23318127276595e-06 relative error = 0.0006798754078611306 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 0.3796050514294296 y[1] (numeric) = 0.3796078850426236 absolute error = 2.833613193975459e-06 relative error = 0.0007464635107739712 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 0.2763720066540575 y[1] (numeric) = 0.2763744103008791 absolute error = 2.403646821524941e-06 relative error = 0.0008697142849686841 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 0.1667110282524814 y[1] (numeric) = 0.166712975094374 absolute error = 1.946841892586093e-06 relative error = 0.001167794304308189 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 0.05157817201918315 y[1] (numeric) = 0.05157963919805161 absolute error = 1.467178868452823e-06 relative error = 0.002844573219669639 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -0.06797780320077421 y[1] (numeric) = -0.0679768341757786 absolute error = 9.690249956062491e-07 relative error = 0.001425502075646971 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -0.19082489910396 y[1] (numeric) = -0.1908244420090399 absolute error = 4.570949201088137e-07 relative error = 0.0002395363090745258 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -0.3157585633478301 y[1] (numeric) = -0.3157586269416242 absolute error = 6.359379400855403e-08 relative error = 2.014000612819517e-05 % Correct digits = 6 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -0.4415134962779729 y[1] (numeric) = -0.4415140840477985 absolute error = 5.877698255885022e-07 relative error = 0.0001331261287692206 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -0.566776463280141 y[1] (numeric) = -0.5667775732415923 absolute error = 1.109961451306596e-06 relative error = 0.0001958376049850141 % Correct digits = 5 h = 0.005 Finished! diff ( y , x , 1 ) = sin(x) * (0.2 * x + 0.3); Iterations = 981 Total Elapsed Time = 49 Seconds Elapsed Time(since restart) = 48 Seconds Time to Timeout = 9 Minutes 11 Seconds Percent Done = 100.2 %