##############ECHO OF PROBLEM################# ##############temp/add_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 + sin(x); ! /* 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(2.0 - cos(x) + x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.104995834721974 y[1] (numeric) = 1.104995834721974 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) = 1.219933422158759 y[1] (numeric) = 1.219933422158773 absolute error = 1.4210854715202e-14 relative error = 1.164887727238007e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.344663510874394 y[1] (numeric) = 1.344663510874423 absolute error = 2.90878432451791e-14 relative error = 2.163206111413267e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.478939005997115 y[1] (numeric) = 1.478939005997159 absolute error = 4.329869796038111e-14 relative error = 2.92768652289272e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.622417438109628 y[1] (numeric) = 1.622417438109684 absolute error = 5.639932965095795e-14 relative error = 3.476252678636891e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.774664385090322 y[1] (numeric) = 1.774664385090391 absolute error = 6.883382752675971e-14 relative error = 3.878695493359798e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.935157812715512 y[1] (numeric) = 1.935157812715593 absolute error = 8.08242361927114e-14 relative error = 4.176622478106563e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 2.103293290652835 y[1] (numeric) = 2.103293290652928 absolute error = 9.237055564881302e-14 relative error = 4.391710659626665e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 2.278390031729337 y[1] (numeric) = 2.278390031729439 absolute error = 1.025846074753645e-13 relative error = 4.502504226526176e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 2.459697694131862 y[1] (numeric) = 2.459697694131972 absolute error = 1.105782132526656e-13 relative error = 4.495601777262049e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 2.655865566747635 y[1] (numeric) = 2.655865566747758 absolute error = 1.230127111284673e-13 relative error = 4.631737113076409e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 2.847306950998193 y[1] (numeric) = 2.847306950998326 absolute error = 1.327826737451687e-13 relative error = 4.66344781333177e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 3.042322285956775 y[1] (numeric) = 3.042322285956917 absolute error = 1.4166445794217e-13 relative error = 4.656457949773659e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 3.239962209804368 y[1] (numeric) = 3.239962209804518 absolute error = 1.501021529293212e-13 relative error = 4.632836533558966e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 3.439251136697356 y[1] (numeric) = 3.439251136697512 absolute error = 1.55875312657372e-13 relative error = 4.532245726232598e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 3.639197004498779 y[1] (numeric) = 3.639197004498939 absolute error = 1.598721155460225e-13 relative error = 4.39306020939203e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 3.838801187135277 y[1] (numeric) = 3.838801187135439 absolute error = 1.620925615952729e-13 relative error = 4.222478677418436e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 4.037068472538712 y[1] (numeric) = 4.037068472538875 absolute error = 1.63424829224823e-13 relative error = 4.048106449927348e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 4.233017006476177 y[1] (numeric) = 4.233017006476342 absolute error = 1.652011860642233e-13 relative error = 3.902681841615064e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 4.42568810291294 y[1] (numeric) = 4.425688102913104 absolute error = 1.643130076445232e-13 relative error = 3.712710968863218e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 4.614155822886393 y[1] (numeric) = 4.614155822886555 absolute error = 1.616484723854228e-13 relative error = 3.503316285584463e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 4.797536226182105 y[1] (numeric) = 4.797536226182262 absolute error = 1.572075802869222e-13 relative error = 3.276839879373427e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 4.97499620337224 y[1] (numeric) = 4.974996203372391 absolute error = 1.509903313490213e-13 relative error = 3.034983850775089e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 5.14576179996958 y[1] (numeric) = 5.145761799969722 absolute error = 1.4210854715202e-13 relative error = 2.761661978851414e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 5.309125949524918 y[1] (numeric) = 5.309125949525053 absolute error = 1.35003119794419e-13 relative error = 2.542850199409936e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 5.464455538401303 y[1] (numeric) = 5.464455538401428 absolute error = 1.243449787580175e-13 relative error = 2.275523661674741e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 5.611197731636212 y[1] (numeric) = 5.611197731636324 absolute error = 1.119104808822158e-13 relative error = 1.994413425341597e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 5.748885496685755 y[1] (numeric) = 5.748885496685858 absolute error = 1.030286966852145e-13 relative error = 1.792150787219728e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 5.877142269859478 y[1] (numeric) = 5.877142269859568 absolute error = 8.970602038971265e-14 relative error = 1.526354412922141e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 5.995685718820274 y[1] (numeric) = 5.99568571882035 absolute error = 7.549516567451064e-14 relative error = 1.259158154963554e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 6.104330563555778 y[1] (numeric) = 6.104330563555842 absolute error = 6.394884621840902e-14 relative error = 1.047598021643814e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 6.202990427634998 y[1] (numeric) = 6.202990427635048 absolute error = 4.973799150320701e-14 relative error = 8.018389208150127e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 6.291678701253065 y[1] (numeric) = 6.2916787012531 absolute error = 3.552713678800501e-14 relative error = 5.64668643694875e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 6.370508407440826 y[1] (numeric) = 6.370508407440849 absolute error = 2.309263891220326e-14 relative error = 3.62492872393525e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 6.439691072776085 y[1] (numeric) = 6.439691072776094 absolute error = 9.769962616701378e-15 relative error = 1.517147718157487e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 6.499534613879955 y[1] (numeric) = 6.499534613879954 absolute error = 1.77635683940025e-15 relative error = 2.733052356713027e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 6.550440260815768 y[1] (numeric) = 6.550440260815755 absolute error = 1.332267629550188e-14 relative error = 2.03385967431794e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 6.592898548130903 y[1] (numeric) = 6.592898548130879 absolute error = 2.398081733190338e-14 relative error = 3.637370900952508e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 6.627484413597747 y[1] (numeric) = 6.627484413597713 absolute error = 3.375077994860476e-14 relative error = 5.092547615707339e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 6.654851453625517 y[1] (numeric) = 6.654851453625473 absolute error = 4.440892098500626e-14 relative error = 6.673164877453814e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 6.675725392740992 y[1] (numeric) = 6.675725392740939 absolute error = 5.240252676230739e-14 relative error = 7.849712754705057e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 6.69089683238893 y[1] (numeric) = 6.690896832388868 absolute error = 6.128431095930864e-14 relative error = 9.159356734159594e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 6.701213351503776 y[1] (numeric) = 6.701213351503706 absolute error = 6.927791673660977e-14 relative error = 1.033811536847481e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 6.707571037781116 y[1] (numeric) = 6.707571037781041 absolute error = 7.460698725481052e-14 relative error = 1.112280240262513e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 6.710905534265635 y[1] (numeric) = 6.710905534265557 absolute error = 7.72715225139109e-14 relative error = 1.151432129678556e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 6.712182690715091 y[1] (numeric) = 6.712182690715009 absolute error = 8.171241461241152e-14 relative error = 1.217374710694982e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 6.712388913148808 y[1] (numeric) = 6.712388913148724 absolute error = 8.348877145181177e-14 relative error = 1.243801164266075e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 6.712521308004792 y[1] (numeric) = 6.712521308004709 absolute error = 8.348877145181177e-14 relative error = 1.243776632071917e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 6.713577719381799 y[1] (numeric) = 6.713577719381719 absolute error = 7.993605777301127e-14 relative error = 1.190662581327381e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 6.71654675891095 y[1] (numeric) = 6.716546758910875 absolute error = 7.549516567451064e-14 relative error = 1.124017570105501e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = 1.0 + sin(x); Iterations = 981 Total Elapsed Time = 21 Seconds Elapsed Time(since restart) = 21 Seconds Time to Timeout = 9 Minutes 39 Seconds Percent Done = 100.2 %