##############ECHO OF PROBLEM################# ##############temp/div_lin_cpostode.ode################# diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0; ! // 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(0.05 * x * x + 0.15 * x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.0155 y[1] (numeric) = 0.0155 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) = 0.03200000000000001 y[1] (numeric) = 0.032 absolute error = 1.387778780781446e-17 relative error = 4.336808689942016e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.04950000000000002 y[1] (numeric) = 0.0495 absolute error = 2.081668171172169e-17 relative error = 4.205390244792257e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.06800000000000005 y[1] (numeric) = 0.06800000000000002 absolute error = 2.775557561562891e-17 relative error = 4.081702296416014e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.08750000000000006 y[1] (numeric) = 0.08750000000000004 absolute error = 2.775557561562891e-17 relative error = 3.172065784643302e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.1080000000000001 y[1] (numeric) = 0.108 absolute error = 5.551115123125783e-17 relative error = 5.139921410301647e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.1295000000000001 y[1] (numeric) = 0.1295 absolute error = 8.326672684688674e-17 relative error = 6.429863076979666e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.1520000000000001 y[1] (numeric) = 0.152 absolute error = 1.110223024625157e-16 relative error = 7.304098846218128e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.1755000000000002 y[1] (numeric) = 0.1755 absolute error = 1.110223024625157e-16 relative error = 6.326057120371257e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.2000000000000002 y[1] (numeric) = 0.2 absolute error = 1.387778780781446e-16 relative error = 6.938893903907222e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.2268012499999996 y[1] (numeric) = 0.22680125 absolute error = 4.440892098500626e-16 relative error = 1.958054507415913e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.253351249999999 y[1] (numeric) = 0.25335125 absolute error = 1.054711873393899e-15 relative error = 4.163041916682483e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.2809012499999984 y[1] (numeric) = 0.28090125 absolute error = 1.609823385706477e-15 relative error = 5.730922826817204e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.3094512499999977 y[1] (numeric) = 0.30945125 absolute error = 2.275957200481571e-15 relative error = 7.354816632608813e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.339001249999997 y[1] (numeric) = 0.3390012499999999 absolute error = 2.886579864025407e-15 relative error = 8.514953452311555e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.3695512499999962 y[1] (numeric) = 0.3695512499999997 absolute error = 3.497202527569243e-15 relative error = 9.463376263966848e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.4011012499999954 y[1] (numeric) = 0.4011012499999996 absolute error = 4.163336342344337e-15 relative error = 1.037976406791149e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.4336512499999945 y[1] (numeric) = 0.4336512499999994 absolute error = 4.884981308350689e-15 relative error = 1.126476934714416e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.4672012499999937 y[1] (numeric) = 0.4672012499999993 absolute error = 5.606626274357041e-15 relative error = 1.20004522127394e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.5017512499999928 y[1] (numeric) = 0.5017512499999991 absolute error = 6.328271240363392e-15 relative error = 1.261236766298735e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.5373012499999918 y[1] (numeric) = 0.5373012499999988 absolute error = 6.994405055138486e-15 relative error = 1.301766012109332e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.5738512499999908 y[1] (numeric) = 0.5738512499999986 absolute error = 7.771561172376096e-15 relative error = 1.354281474925117e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.6114012499999898 y[1] (numeric) = 0.6114012499999983 absolute error = 8.548717289613705e-15 relative error = 1.39821717564592e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.6499512499999887 y[1] (numeric) = 0.6499512499999981 absolute error = 9.436895709313831e-15 relative error = 1.451939004550571e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.6895012499999875 y[1] (numeric) = 0.6895012499999977 absolute error = 1.021405182655144e-14 relative error = 1.481368137701219e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.7300512499999863 y[1] (numeric) = 0.7300512499999974 absolute error = 1.110223024625157e-14 relative error = 1.520746693639902e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.7716012499999851 y[1] (numeric) = 0.771601249999997 absolute error = 1.187938636348917e-14 relative error = 1.539575831880703e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.8141512499999838 y[1] (numeric) = 0.8141512499999967 absolute error = 1.287858708565182e-14 relative error = 1.581842082248485e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.8577012499999825 y[1] (numeric) = 0.8577012499999963 absolute error = 1.376676550535194e-14 relative error = 1.605077001502822e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.9022512499999812 y[1] (numeric) = 0.902251249999996 absolute error = 1.476596622751458e-14 relative error = 1.636569218110243e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.9478012499999797 y[1] (numeric) = 0.9478012499999956 absolute error = 1.587618925213974e-14 relative error = 1.675054686005118e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.9943512499999783 y[1] (numeric) = 0.9943512499999951 absolute error = 1.687538997430238e-14 relative error = 1.697125635865872e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.041901249999977 y[1] (numeric) = 1.041901249999994 absolute error = 1.754152378907747e-14 relative error = 1.683607135424577e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.090451249999975 y[1] (numeric) = 1.090451249999994 absolute error = 1.887379141862766e-14 relative error = 1.730823951884882e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.140001249999974 y[1] (numeric) = 1.140001249999994 absolute error = 1.998401444325282e-14 relative error = 1.752981800963225e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 1.190551249999972 y[1] (numeric) = 1.190551249999993 absolute error = 2.087219286295294e-14 relative error = 1.753153664149563e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.24210124999997 y[1] (numeric) = 1.242101249999993 absolute error = 2.220446049250313e-14 relative error = 1.787653018826256e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.294651249999969 y[1] (numeric) = 1.294651249999992 absolute error = 2.331468351712829e-14 relative error = 1.800846638593123e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 1.348201249999967 y[1] (numeric) = 1.348201249999991 absolute error = 2.442490654175344e-14 relative error = 1.811666213909388e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 1.402751249999965 y[1] (numeric) = 1.402751249999991 absolute error = 2.575717417130363e-14 relative error = 1.83618971441332e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.458301249999963 y[1] (numeric) = 1.45830124999999 absolute error = 2.664535259100376e-14 relative error = 1.827150089256553e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.514851249999962 y[1] (numeric) = 1.51485124999999 absolute error = 2.797762022055394e-14 relative error = 1.846888941772643e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.57240124999996 y[1] (numeric) = 1.572401249999989 absolute error = 2.930988785010413e-14 relative error = 1.864020894800541e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 1.630951249999958 y[1] (numeric) = 1.630951249999988 absolute error = 3.042011087472929e-14 relative error = 1.865175974740513e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 1.690501249999956 y[1] (numeric) = 1.690501249999987 absolute error = 3.175237850427948e-14 relative error = 1.878281870793074e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 1.751051249999954 y[1] (numeric) = 1.751051249999987 absolute error = 3.308464613382966e-14 relative error = 1.88941620833945e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 1.812601249999952 y[1] (numeric) = 1.812601249999986 absolute error = 3.441691376337985e-14 relative error = 1.898758139076687e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.875151249999949 y[1] (numeric) = 1.875151249999985 absolute error = 3.574918139293004e-14 relative error = 1.906469219105979e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.938701249999947 y[1] (numeric) = 1.938701249999984 absolute error = 3.730349362740526e-14 relative error = 1.924148634422466e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.003251249999945 y[1] (numeric) = 2.003251249999983 absolute error = 3.819167204710538e-14 relative error = 1.906484373695333e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0; Iterations = 981 Total Elapsed Time = 43 Seconds Elapsed Time(since restart) = 43 Seconds Time to Timeout = 9 Minutes 17 Seconds Percent Done = 100.2 %