##############ECHO OF PROBLEM################# ##############temp/mult_c_sinpostode.ode################# diff ( y , x , 1 ) = 2.0 * 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(-cos(x) * 2.0); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -1.990008330556052 y[1] (numeric) = -1.990008330556052 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) = -1.960133155682483 y[1] (numeric) = -1.960133155682453 absolute error = 2.997602166487923e-14 relative error = 1.529284966073752e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -1.910672978251212 y[1] (numeric) = -1.910672978251153 absolute error = 5.928590951498336e-14 relative error = 3.102881036672543e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -1.84212198800577 y[1] (numeric) = -1.842121988005682 absolute error = 8.79296635503124e-14 relative error = 4.773281255141121e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -1.755165123780745 y[1] (numeric) = -1.75516512378063 absolute error = 1.154631945610163e-13 relative error = 6.578480451588549e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -1.650671229819356 y[1] (numeric) = -1.650671229819215 absolute error = 1.412203687323199e-13 relative error = 8.555329867097435e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -1.529684374568976 y[1] (numeric) = -1.529684374568811 absolute error = 1.649791414592983e-13 relative error = 1.07851753081929e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -1.39341341869433 y[1] (numeric) = -1.393413418694143 absolute error = 1.871836019518014e-13 relative error = 1.343345768316183e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -1.243219936541328 y[1] (numeric) = -1.243219936541121 absolute error = 2.071676163950542e-13 relative error = 1.666379457937267e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -1.080604611736278 y[1] (numeric) = -1.080604611736054 absolute error = 2.244870955792067e-13 relative error = 2.077421224572681e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.8982688665047259 y[1] (numeric) = -0.898268866504482 absolute error = 2.439159985101469e-13 relative error = 2.715400784836882e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.7153860980036061 y[1] (numeric) = -0.7153860980033457 absolute error = 2.603472992745992e-13 relative error = 3.639255780915201e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -0.5253554280864383 y[1] (numeric) = -0.5253554280861648 absolute error = 2.735589532676386e-13 relative error = 5.207121477055131e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -0.330075580391247 y[1] (numeric) = -0.3300755803909628 absolute error = 2.842170943040401e-13 relative error = 8.610667107428858e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -0.1314977266052671 y[1] (numeric) = -0.131497726604975 absolute error = 2.921274333544943e-13 relative error = 2.221539800694875e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.06839400899758327 y[1] (numeric) = 0.0683940089978802 absolute error = 2.969291479359981e-13 relative error = 4.341449672097599e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.2676023742705834 y[1] (numeric) = 0.267602374270882 absolute error = 2.986499936241671e-13 relative error = 1.116021464451546e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.4641369450774562 y[1] (numeric) = 0.4641369450777534 absolute error = 2.972067036921544e-13 relative error = 6.403426980857038e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.6560340129523912 y[1] (numeric) = 0.656034012952684 absolute error = 2.928768338961163e-13 relative error = 4.464354410193829e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.8413762058259195 y[1] (numeric) = 0.8413762058262048 absolute error = 2.852162950262027e-13 relative error = 3.389878309503964e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.018311645772832 y[1] (numeric) = 1.018311645773107 absolute error = 2.748912208971888e-13 relative error = 2.699480282272176e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.185072452364259 y[1] (numeric) = 1.18507245236452 absolute error = 2.613464999967618e-13 relative error = 2.205320860132787e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.339992406744534 y[1] (numeric) = 1.33999240674478 absolute error = 2.460254222569347e-13 relative error = 1.836021017870132e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 1.481523599939217 y[1] (numeric) = 1.481523599939444 absolute error = 2.275957200481571e-13 relative error = 1.5362274354421e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 1.608251899049899 y[1] (numeric) = 1.608251899050106 absolute error = 2.071676163950542e-13 relative error = 1.288154029337331e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 1.718911076802673 y[1] (numeric) = 1.718911076802858 absolute error = 1.84519066692701e-13 relative error = 1.073464876588746e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 1.812395463272495 y[1] (numeric) = 1.812395463272654 absolute error = 1.598721155460225e-13 relative error = 8.821039270168691e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 1.887770993371586 y[1] (numeric) = 1.887770993371719 absolute error = 1.338928967697939e-13 relative error = 7.092645095190242e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 1.944284539719035 y[1] (numeric) = 1.94428453971914 absolute error = 1.054711873393899e-13 relative error = 5.424678599493022e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 1.981371437640632 y[1] (numeric) = 1.981371437640709 absolute error = 7.66053886991358e-14 relative error = 3.866281063905695e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 1.998661127111645 y[1] (numeric) = 1.998661127111691 absolute error = 4.685141163918161e-14 relative error = 2.344139834594607e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 1.995980855270089 y[1] (numeric) = 1.995980855270105 absolute error = 1.643130076445232e-14 relative error = 8.232193570929263e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.973357402506225 y[1] (numeric) = 1.973357402506212 absolute error = 1.376676550535194e-14 relative error = 6.976316346885627e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.931016814881752 y[1] (numeric) = 1.931016814881708 absolute error = 4.440892098500626e-14 relative error = 2.299768735453797e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.869382145552275 y[1] (numeric) = 1.8693821455522 absolute error = 7.460698725481052e-14 relative error = 3.990997102027485e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 1.789069227760021 y[1] (numeric) = 1.789069227759917 absolute error = 1.043609643147647e-13 relative error = 5.833254672063663e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.690880521631649 y[1] (numeric) = 1.690880521631516 absolute error = 1.336708521648688e-13 relative error = 7.905399018724306e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.575797096261924 y[1] (numeric) = 1.575797096261763 absolute error = 1.609823385706477e-13 relative error = 1.021593065201903e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 1.444968827195616 y[1] (numeric) = 1.44496882719543 absolute error = 1.867395127419513e-13 relative error = 1.292342846623023e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 1.299702907251161 y[1] (numeric) = 1.29970290725095 absolute error = 2.107203300738547e-13 relative error = 1.621296135433927e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.141450785482113 y[1] (numeric) = 1.141450785481881 absolute error = 2.329247905663578e-13 relative error = 2.040603007408485e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 0.9717936647779938 y[1] (numeric) = 0.9717936647777411 absolute error = 2.526867604046856e-13 relative error = 2.600209998924122e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 0.7924267030076897 y[1] (numeric) = 0.7924267030074198 absolute error = 2.698952172863756e-13 relative error = 3.405932892745495e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 0.6051420755623752 y[1] (numeric) = 0.6051420755620907 absolute error = 2.845501612114276e-13 relative error = 4.702204204640494e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 0.4118110685314167 y[1] (numeric) = 0.4118110685311202 absolute error = 2.965405698773793e-13 relative error = 7.200888770058799e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 0.2143653814303334 y[1] (numeric) = 0.2143653814300278 absolute error = 3.055888875280743e-13 relative error = 1.425551483588723e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 0.01477782629777229 y[1] (numeric) = 0.01477782629746067 absolute error = 3.116205210540457e-13 relative error = 2.108703369324495e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -0.1849573839902562 y[1] (numeric) = -0.1849573839905708 absolute error = 3.146094496031537e-13 relative error = 1.700983452597533e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -0.3828445612362367 y[1] (numeric) = -0.3828445612365513 absolute error = 3.145261828763068e-13 relative error = 8.215506101501763e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -0.5769064821779314 y[1] (numeric) = -0.5769064821782429 absolute error = 3.115285807098189e-13 relative error = 5.39998405865955e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = 2.0 * sin(x); Iterations = 981 Total Elapsed Time = 49 Seconds Elapsed Time(since restart) = 48 Seconds Time to Timeout = 9 Minutes 11 Seconds Percent Done = 100.2 %