##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin(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(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(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) = 1.363309554731651 y[1] (numeric) = 1.363309554731651 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) = 1.460293443195882 y[1] (numeric) = 1.460293443195892 absolute error = 9.547918011776346e-15 relative error = 6.538355736830902e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.555816641869629 y[1] (numeric) = 1.555816641869646 absolute error = 1.709743457922741e-14 relative error = 1.09893634758151e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.649650988248791 y[1] (numeric) = 1.649650988248814 absolute error = 2.287059430727822e-14 relative error = 1.386389877022218e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.741591099919966 y[1] (numeric) = 1.741591099919994 absolute error = 2.797762022055394e-14 relative error = 1.606440238574924e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.831452007332497 y[1] (numeric) = 1.831452007332529 absolute error = 3.219646771412954e-14 relative error = 1.757974961136087e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.919067137385126 y[1] (numeric) = 1.919067137385161 absolute error = 3.530509218307998e-14 relative error = 1.839700732470769e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 2.004286579715731 y[1] (numeric) = 2.004286579715769 absolute error = 3.774758283725532e-14 relative error = 1.883342592784764e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 2.086975583471242 y[1] (numeric) = 2.086975583471282 absolute error = 4.04121180963557e-14 relative error = 1.936396305563801e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 2.167013243972269 y[1] (numeric) = 2.167013243972311 absolute error = 4.174438572590589e-14 relative error = 1.926355819099003e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 2.248081035088911 y[1] (numeric) = 2.248081035088955 absolute error = 4.39648317751562e-14 relative error = 1.955660453913192e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 2.322357892539673 y[1] (numeric) = 2.322357892539721 absolute error = 4.796163466380676e-14 relative error = 2.065212894958111e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 2.39368883637177 y[1] (numeric) = 2.393688836371822 absolute error = 5.151434834260726e-14 relative error = 2.15209042879149e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 2.461998497487226 y[1] (numeric) = 2.46199849748728 absolute error = 5.329070518200751e-14 relative error = 2.164530369794996e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 2.527220681225443 y[1] (numeric) = 2.527220681225498 absolute error = 5.506706202140776e-14 relative error = 2.178957398952033e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 2.589297708395291 y[1] (numeric) = 2.589297708395348 absolute error = 5.684341886080801e-14 relative error = 2.195321869575072e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 2.648179817414706 y[1] (numeric) = 2.648179817414765 absolute error = 5.995204332975845e-14 relative error = 2.263896240561445e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 2.703824619842736 y[1] (numeric) = 2.703824619842798 absolute error = 6.17284001691587e-14 relative error = 2.283003110340383e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 2.756196602802734 y[1] (numeric) = 2.756196602802798 absolute error = 6.439293542825908e-14 relative error = 2.336296886904907e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 2.80526667278501 y[1] (numeric) = 2.805266672785075 absolute error = 6.572520305780927e-14 relative error = 2.342921751270038e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 2.851011736129775 y[1] (numeric) = 2.851011736129843 absolute error = 6.794564910705958e-14 relative error = 2.38321183480273e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 2.893414312162552 y[1] (numeric) = 2.893414312162623 absolute error = 7.105427357601002e-14 relative error = 2.45572413453999e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 2.932462175512369 y[1] (numeric) = 2.932462175512441 absolute error = 7.238654120556021e-14 relative error = 2.468456091608841e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.968148024609695 y[1] (numeric) = 2.968148024609769 absolute error = 7.416289804496046e-14 relative error = 2.498625318887616e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 3.000469173753358 y[1] (numeric) = 3.000469173753433 absolute error = 7.505107646466058e-14 relative error = 2.501311365608113e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 3.029427266467097 y[1] (numeric) = 3.029427266467172 absolute error = 7.505107646466058e-14 relative error = 2.477401497484532e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 3.055028008147787 y[1] (numeric) = 3.055028008147862 absolute error = 7.593925488436071e-14 relative error = 2.485713868476166e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 3.07728091624735 y[1] (numeric) = 3.077280916247427 absolute error = 7.682743330406083e-14 relative error = 2.49660123320004e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 3.09619908643594 y[1] (numeric) = 3.096199086436018 absolute error = 7.771561172376096e-14 relative error = 2.510032770961768e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 3.11179897337075 y[1] (numeric) = 3.111798973370826 absolute error = 7.593925488436071e-14 relative error = 2.440365060025137e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 3.124100184847515 y[1] (numeric) = 3.124100184847592 absolute error = 7.682743330406083e-14 relative error = 2.459185965824291e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 3.133125288244074 y[1] (numeric) = 3.133125288244151 absolute error = 7.72715225139109e-14 relative error = 2.466276174905756e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 3.138899628280455 y[1] (numeric) = 3.138899628280531 absolute error = 7.638334409421077e-14 relative error = 2.433443344477215e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 3.141451155220426 y[1] (numeric) = 3.141451155220503 absolute error = 7.682743330406083e-14 relative error = 2.445603305860411e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 3.140810262727402 y[1] (numeric) = 3.140810262727479 absolute error = 7.72715225139109e-14 relative error = 2.460241659004585e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 3.137009634664879 y[1] (numeric) = 3.137009634664957 absolute error = 7.72715225139109e-14 relative error = 2.46322235226943e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.130084100199652 y[1] (numeric) = 3.130084100199729 absolute error = 7.638334409421077e-14 relative error = 2.440296862609495e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 3.120070496626199 y[1] (numeric) = 3.120070496626275 absolute error = 7.638334409421077e-14 relative error = 2.448128789936181e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 3.107007539383932 y[1] (numeric) = 3.107007539384008 absolute error = 7.638334409421077e-14 relative error = 2.45842158816764e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 3.090935698786344 y[1] (numeric) = 3.09093569878642 absolute error = 7.593925488436071e-14 relative error = 2.456837096746408e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 3.071897083023255 y[1] (numeric) = 3.071897083023331 absolute error = 7.638334409421077e-14 relative error = 2.486520284691209e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 3.049935327034975 y[1] (numeric) = 3.049935327035052 absolute error = 7.682743330406083e-14 relative error = 2.518985652681015e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 3.025095486890944 y[1] (numeric) = 3.025095486891021 absolute error = 7.638334409421077e-14 relative error = 2.524989522651865e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 2.997423939335557 y[1] (numeric) = 2.997423939335634 absolute error = 7.72715225139109e-14 relative error = 2.577931052723886e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 2.966968286191096 y[1] (numeric) = 2.966968286191172 absolute error = 7.593925488436071e-14 relative error = 2.559489942571959e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 2.933777263332135 y[1] (numeric) = 2.93377726333221 absolute error = 7.505107646466058e-14 relative error = 2.558172271722456e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.897900653967863 y[1] (numeric) = 2.897900653967938 absolute error = 7.416289804496046e-14 relative error = 2.559193944189051e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 2.859389205988768 y[1] (numeric) = 2.859389205988841 absolute error = 7.283063041541027e-14 relative error = 2.547069502216494e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 2.818294553152187 y[1] (numeric) = 2.81829455315226 absolute error = 7.238654120556021e-14 relative error = 2.568451942845995e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.774669139897724 y[1] (numeric) = 2.774669139897795 absolute error = 7.105427357601002e-14 relative error = 2.560819686725932e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sin(sqrt(2.0*x + 3.0)); Iterations = 981 Total Elapsed Time = 1 Minutes 53 Seconds Elapsed Time(since restart) = 1 Minutes 52 Seconds Time to Timeout = 8 Minutes 7 Seconds Percent Done = 100.2 %