##############ECHO OF PROBLEM################# ##############temp/div_c_linpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(2.5); x_end=c(3.1); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(10.0) * ln(c(0.2) * c(x) + c(0.3))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -2.231435513142097 y[1] (numeric) = -2.231435513142097 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999999 y[1] (closed_form) = -2.206466711156228 y[1] (numeric) = -2.206466711156225 absolute error = 3.108624468950438e-15 relative error = 1.408869870201424e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999998 y[1] (closed_form) = -2.181560098031712 y[1] (numeric) = -2.181560098031706 absolute error = 5.329070518200751e-15 relative error = 2.442779606671779e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999997 y[1] (closed_form) = -2.156715364755095 y[1] (numeric) = -2.156715364755088 absolute error = 7.549516567451064e-15 relative error = 3.500469598735551e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999996 y[1] (closed_form) = -2.131932204610427 y[1] (numeric) = -2.131932204610417 absolute error = 1.021405182655144e-14 relative error = 4.790983411415691e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999994 y[1] (closed_form) = -2.107210313156539 y[1] (numeric) = -2.107210313156526 absolute error = 1.332267629550188e-14 relative error = 6.322423638647108e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999993 y[1] (closed_form) = -2.082549388204607 y[1] (numeric) = -2.082549388204591 absolute error = 1.554312234475219e-14 relative error = 7.463507195933596e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999992 y[1] (closed_form) = -2.057949129795986 y[1] (numeric) = -2.057949129795968 absolute error = 1.731947918415244e-14 relative error = 8.415892761095317e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999991 y[1] (closed_form) = -2.033409240180321 y[1] (numeric) = -2.033409240180301 absolute error = 1.998401444325282e-14 relative error = 9.82783693924822e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58999999999999 y[1] (closed_form) = -2.008929423793924 y[1] (numeric) = -2.0089294237939 absolute error = 2.353672812205332e-14 relative error = 1.171605524976756e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999989 y[1] (closed_form) = -1.984509387238409 y[1] (numeric) = -1.984509387238383 absolute error = 2.642330798607873e-14 relative error = 1.331478105167782e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999988 y[1] (closed_form) = -1.9601488392596 y[1] (numeric) = -1.960148839259571 absolute error = 2.90878432451791e-14 relative error = 1.483960945341597e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999987 y[1] (closed_form) = -1.935847490726685 y[1] (numeric) = -1.935847490726654 absolute error = 3.153033389935445e-14 relative error = 1.628761255749464e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999986 y[1] (closed_form) = -1.911605054611624 y[1] (numeric) = -1.91160505461159 absolute error = 3.375077994860476e-14 relative error = 1.765572855500836e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.639999999999985 y[1] (closed_form) = -1.88742124596881 y[1] (numeric) = -1.887421245968774 absolute error = 3.61932706027801e-14 relative error = 1.917604280447853e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999983 y[1] (closed_form) = -1.863295781914974 y[1] (numeric) = -1.863295781914935 absolute error = 3.885780586188048e-14 relative error = 2.085434112985807e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999982 y[1] (closed_form) = -1.839228381609326 y[1] (numeric) = -1.839228381609284 absolute error = 4.174438572590589e-14 relative error = 2.269668418740881e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999981 y[1] (closed_form) = -1.815218766233947 y[1] (numeric) = -1.815218766233902 absolute error = 4.485301019485632e-14 relative error = 2.470942402601606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67999999999998 y[1] (closed_form) = -1.791266658974401 y[1] (numeric) = -1.791266658974354 absolute error = 4.729550084903167e-14 relative error = 2.640338366824231e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999979 y[1] (closed_form) = -1.76737178500059 y[1] (numeric) = -1.76737178500054 absolute error = 4.996003610813204e-14 relative error = 2.82679833027409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999978 y[1] (closed_form) = -1.743533871447829 y[1] (numeric) = -1.743533871447777 absolute error = 5.240252676230739e-14 relative error = 3.005535345223455e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999977 y[1] (closed_form) = -1.719752647398157 y[1] (numeric) = -1.719752647398102 absolute error = 5.506706202140776e-14 relative error = 3.202033856713036e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999976 y[1] (closed_form) = -1.696027843861856 y[1] (numeric) = -1.696027843861798 absolute error = 5.795364188543317e-14 relative error = 3.417021842841489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.729999999999975 y[1] (closed_form) = -1.672359193759197 y[1] (numeric) = -1.672359193759136 absolute error = 6.084022174945858e-14 relative error = 3.637987698844735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999974 y[1] (closed_form) = -1.648746431902402 y[1] (numeric) = -1.648746431902339 absolute error = 6.306066779870889e-14 relative error = 3.824764474301031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999972 y[1] (closed_form) = -1.625189294977814 y[1] (numeric) = -1.625189294977748 absolute error = 6.59472476627343e-14 relative error = 4.057819471647122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999971 y[1] (closed_form) = -1.60168752152828 y[1] (numeric) = -1.601687521528212 absolute error = 6.816769371198461e-14 relative error = 4.255992058110133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76999999999997 y[1] (closed_form) = -1.578240851935741 y[1] (numeric) = -1.57824085193567 absolute error = 7.105427357601002e-14 relative error = 4.502118513081236e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999969 y[1] (closed_form) = -1.554849028404021 y[1] (numeric) = -1.554849028403948 absolute error = 7.349676423018536e-14 relative error = 4.726938943109242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999968 y[1] (closed_form) = -1.531511794941822 y[1] (numeric) = -1.531511794941746 absolute error = 7.593925488436071e-14 relative error = 4.958450541169057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999967 y[1] (closed_form) = -1.508228897345913 y[1] (numeric) = -1.508228897345834 absolute error = 7.860379014346108e-14 relative error = 5.211661855954567e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999966 y[1] (closed_form) = -1.485000083184518 y[1] (numeric) = -1.485000083184437 absolute error = 8.104628079763643e-14 relative error = 5.457661700855679e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.819999999999965 y[1] (closed_form) = -1.461825101780895 y[1] (numeric) = -1.461825101780812 absolute error = 8.348877145181177e-14 relative error = 5.711269518501224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999964 y[1] (closed_form) = -1.438703704197102 y[1] (numeric) = -1.438703704197016 absolute error = 8.593126210598712e-14 relative error = 5.972825527264684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999963 y[1] (closed_form) = -1.415635643217954 y[1] (numeric) = -1.415635643217866 absolute error = 8.837375276016246e-14 relative error = 6.242690566852041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999961 y[1] (closed_form) = -1.392620673335164 y[1] (numeric) = -1.392620673335073 absolute error = 9.103828801926284e-14 relative error = 6.537192055409943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85999999999996 y[1] (closed_form) = -1.369658550731665 y[1] (numeric) = -1.369658550731571 absolute error = 9.370282327836321e-14 relative error = 6.841327221905608e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999959 y[1] (closed_form) = -1.346749033266109 y[1] (numeric) = -1.346749033266012 absolute error = 9.636735853746359e-14 relative error = 7.155554313171135e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999958 y[1] (closed_form) = -1.323891880457551 y[1] (numeric) = -1.323891880457452 absolute error = 9.880984919163893e-14 relative error = 7.463589032473649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999957 y[1] (closed_form) = -1.301086853470301 y[1] (numeric) = -1.3010868534702 absolute error = 1.016964290556643e-13 relative error = 7.81626751391856e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999956 y[1] (closed_form) = -1.278333715098948 y[1] (numeric) = -1.278333715098845 absolute error = 1.039168751049147e-13 relative error = 8.129088193286918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999955 y[1] (closed_form) = -1.255632229753559 y[1] (numeric) = -1.255632229753453 absolute error = 1.0635936575909e-13 relative error = 8.4705826466373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999954 y[1] (closed_form) = -1.23298216344504 y[1] (numeric) = -1.232982163444931 absolute error = 1.090239010181904e-13 relative error = 8.842293445151695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999953 y[1] (closed_form) = -1.210383283770667 y[1] (numeric) = -1.210383283770556 absolute error = 1.114663916723657e-13 relative error = 9.209181353291506e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999952 y[1] (closed_form) = -1.187835359899778 y[1] (numeric) = -1.187835359899664 absolute error = 1.139088823265411e-13 relative error = 9.589618744482562e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94999999999995 y[1] (closed_form) = -1.165338162559626 y[1] (numeric) = -1.16533816255951 absolute error = 1.163513729807164e-13 relative error = 9.984344177414951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999949 y[1] (closed_form) = -1.14289146402139 y[1] (numeric) = -1.142891464021271 absolute error = 1.192379528447418e-13 relative error = 1.043300756006961e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999948 y[1] (closed_form) = -1.120495038086345 y[1] (numeric) = -1.120495038086223 absolute error = 1.216804434989172e-13 relative error = 1.085952542072217e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999947 y[1] (closed_form) = -1.098148660072183 y[1] (numeric) = -1.098148660072059 absolute error = 1.241229341530925e-13 relative error = 1.130292634013082e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999946 y[1] (closed_form) = -1.075852106799494 y[1] (numeric) = -1.075852106799367 absolute error = 1.267874694121929e-13 relative error = 1.178484185799175e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999945 y[1] (closed_form) = -1.053605156578385 y[1] (numeric) = -1.053605156578255 absolute error = 1.298960938811433e-13 relative error = 1.232872609536051e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.009999999999944 y[1] (closed_form) = -1.031407589195258 y[1] (numeric) = -1.031407589195126 absolute error = 1.323385845353187e-13 relative error = 1.283087170597359e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999943 y[1] (closed_form) = -1.009259185899732 y[1] (numeric) = -1.009259185899597 absolute error = 1.35003119794419e-13 relative error = 1.33764568785239e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999942 y[1] (closed_form) = -0.9871597293917056 y[1] (numeric) = -0.9871597293915682 absolute error = 1.374456104485944e-13 relative error = 1.392334050471136e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999941 y[1] (closed_form) = -0.9651090038085681 y[1] (numeric) = -0.9651090038084283 absolute error = 1.397770788003072e-13 relative error = 1.448303541348293e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999939 y[1] (closed_form) = -0.9431067947125459 y[1] (numeric) = -0.9431067947124038 absolute error = 1.4210854715202e-13 relative error = 1.506812886395692e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999938 y[1] (closed_form) = -0.9211528890781915 y[1] (numeric) = -0.9211528890780469 absolute error = 1.445510378061954e-13 relative error = 1.569240454218727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999937 y[1] (closed_form) = -0.8992470752800074 y[1] (numeric) = -0.8992470752798605 absolute error = 1.468825061579082e-13 relative error = 1.633394316152454e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999936 y[1] (closed_form) = -0.8773891430802068 y[1] (numeric) = -0.8773891430800574 absolute error = 1.493249968120836e-13 relative error = 1.701924374033803e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999935 y[1] (closed_form) = -0.8555788836166069 y[1] (numeric) = -0.8555788836164554 absolute error = 1.515454428613339e-13 relative error = 1.771262074874242e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.099999999999934 y[1] (closed_form) = -0.8338160893906538 y[1] (numeric) = -0.8338160893904998 absolute error = 1.539879335155092e-13 relative error = 1.846785346011281e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations = 601 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %