##############ECHO OF PROBLEM################# ##############temp/arcsin_c_arccos_c_arctan_cpostode.ode################# diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(0.1); ! /* 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((arcsin(0.1) + arccos(0.1) + arctan(0.1)) * x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.1670464979286059 y[1] (numeric) = 0.1670464979286059 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) = 0.3340929958572119 y[1] (numeric) = 0.3340929958572116 absolute error = 2.775557561562891e-16 relative error = 8.307739449734343e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.5011394937858178 y[1] (numeric) = 0.5011394937858173 absolute error = 4.440892098500626e-16 relative error = 8.861588746383299e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.6681859917144238 y[1] (numeric) = 0.6681859917144242 absolute error = 3.33066907387547e-16 relative error = 4.984643669840605e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.8352324896430299 y[1] (numeric) = 0.835232489643031 absolute error = 1.110223024625157e-15 relative error = 1.329238311957495e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.002278987571636 y[1] (numeric) = 1.002278987571638 absolute error = 1.998401444325282e-15 relative error = 1.993857467936242e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.169325485500242 y[1] (numeric) = 1.169325485500245 absolute error = 2.664535259100376e-15 relative error = 2.27869424906999e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.336371983428848 y[1] (numeric) = 1.336371983428851 absolute error = 3.552713678800501e-15 relative error = 2.658476623914989e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 1.503418481357454 y[1] (numeric) = 1.503418481357458 absolute error = 4.440892098500626e-15 relative error = 2.953862915461099e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.67046497928606 y[1] (numeric) = 1.670464979286065 absolute error = 5.329070518200751e-15 relative error = 3.190171948697987e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.845863802111092 y[1] (numeric) = 1.845863802111102 absolute error = 1.021405182655144e-14 relative error = 5.53348075566017e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 2.012910300039695 y[1] (numeric) = 2.012910300039709 absolute error = 1.4210854715202e-14 relative error = 7.059854934878005e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 2.179956797968297 y[1] (numeric) = 2.179956797968311 absolute error = 1.465494392505207e-14 relative error = 6.722584566221846e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 2.347003295896899 y[1] (numeric) = 2.347003295896914 absolute error = 1.465494392505207e-14 relative error = 6.244108796384e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 2.514049793825501 y[1] (numeric) = 2.514049793825516 absolute error = 1.465494392505207e-14 relative error = 5.829217846458158e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 2.681096291754104 y[1] (numeric) = 2.681096291754118 absolute error = 1.465494392505207e-14 relative error = 5.466026703376658e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 2.848142789682706 y[1] (numeric) = 2.848142789682721 absolute error = 1.465494392505207e-14 relative error = 5.145438626932283e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 3.015189287611308 y[1] (numeric) = 3.015189287611323 absolute error = 1.509903313490213e-14 relative error = 5.007656798510278e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 3.18223578553991 y[1] (numeric) = 3.182235785539925 absolute error = 1.509903313490213e-14 relative error = 4.744787675228902e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 3.349282283468513 y[1] (numeric) = 3.349282283468528 absolute error = 1.465494392505207e-14 relative error = 4.375547560558384e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 3.516328781397116 y[1] (numeric) = 3.51632878139713 absolute error = 1.465494392505207e-14 relative error = 4.167683068370339e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 3.683375279325718 y[1] (numeric) = 3.683375279325733 absolute error = 1.465494392505207e-14 relative error = 3.978672498376221e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 3.85042177725432 y[1] (numeric) = 3.850421777254335 absolute error = 1.509903313490213e-14 relative error = 3.92139718928897e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 4.017468275182923 y[1] (numeric) = 4.017468275182938 absolute error = 1.509903313490213e-14 relative error = 3.758345331106477e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 4.184514773111525 y[1] (numeric) = 4.18451477311154 absolute error = 1.509903313490213e-14 relative error = 3.608311585353725e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 4.351561271040127 y[1] (numeric) = 4.351561271040143 absolute error = 1.598721155460225e-14 relative error = 3.673902436120572e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 4.518607768968729 y[1] (numeric) = 4.518607768968745 absolute error = 1.598721155460225e-14 relative error = 3.538083492086541e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 4.685654266897331 y[1] (numeric) = 4.685654266897347 absolute error = 1.598721155460225e-14 relative error = 3.411948608233189e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 4.852700764825934 y[1] (numeric) = 4.85270076482595 absolute error = 1.598721155460225e-14 relative error = 3.294497709498829e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 5.019747262754536 y[1] (numeric) = 5.019747262754552 absolute error = 1.598721155460225e-14 relative error = 3.18486384229421e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 5.186793760683138 y[1] (numeric) = 5.186793760683154 absolute error = 1.598721155460225e-14 relative error = 3.082291737872497e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 5.353840258611741 y[1] (numeric) = 5.353840258611757 absolute error = 1.598721155460225e-14 relative error = 2.986120388796913e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 5.520886756540343 y[1] (numeric) = 5.520886756540359 absolute error = 1.598721155460225e-14 relative error = 2.895768788530743e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 5.687933254468946 y[1] (numeric) = 5.687933254468962 absolute error = 1.598721155460225e-14 relative error = 2.810724183874922e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 5.854979752397548 y[1] (numeric) = 5.854979752397564 absolute error = 1.598721155460225e-14 relative error = 2.730532338400602e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 6.02202625032615 y[1] (numeric) = 6.022026250326166 absolute error = 1.598721155460225e-14 relative error = 2.654789416392264e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 6.189072748254752 y[1] (numeric) = 6.189072748254769 absolute error = 1.687538997430238e-14 relative error = 2.726642691194904e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 6.356119246183354 y[1] (numeric) = 6.356119246183371 absolute error = 1.687538997430238e-14 relative error = 2.654983224934854e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 6.523165744111957 y[1] (numeric) = 6.523165744111973 absolute error = 1.687538997430238e-14 relative error = 2.586993897791837e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 6.690212242040559 y[1] (numeric) = 6.690212242040576 absolute error = 1.687538997430238e-14 relative error = 2.522399792978059e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 6.857258739969161 y[1] (numeric) = 6.857258739969178 absolute error = 1.687538997430238e-14 relative error = 2.460952782186876e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 7.024305237897764 y[1] (numeric) = 7.024305237897781 absolute error = 1.687538997430238e-14 relative error = 2.402428340279935e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 7.191351735826366 y[1] (numeric) = 7.191351735826383 absolute error = 1.687538997430238e-14 relative error = 2.346622803920355e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 7.358398233754968 y[1] (numeric) = 7.358398233754985 absolute error = 1.687538997430238e-14 relative error = 2.293351003604343e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 7.525444731683571 y[1] (numeric) = 7.525444731683588 absolute error = 1.687538997430238e-14 relative error = 2.242444211071505e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 7.692491229612173 y[1] (numeric) = 7.69249122961219 absolute error = 1.687538997430238e-14 relative error = 2.193748354153557e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 7.859537727540776 y[1] (numeric) = 7.859537727540792 absolute error = 1.687538997430238e-14 relative error = 2.147122459272504e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 8.026584225469378 y[1] (numeric) = 8.026584225469396 absolute error = 1.77635683940025e-14 relative error = 2.213091882551538e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 8.19363072339798 y[1] (numeric) = 8.193630723397998 absolute error = 1.77635683940025e-14 relative error = 2.167972781989835e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 8.360677221326583 y[1] (numeric) = 8.360677221326601 absolute error = 1.77635683940025e-14 relative error = 2.124656642489539e-13 % Correct digits = 14 h = 0.005 Finished! diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(0.1); Iterations = 981 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Time to Timeout = 9 Minutes 43 Seconds Percent Done = 100.2 %