Prog: testbulirsch.c Gragg-Bulirsch-Stoer Method for the solution of a diffeq Gragg_Bulirsch_Stoer Method Problem: Solve y' = xy, Initial condition x = 0.0, y = 1.0 Number of steps 10 and step size 0.10 Polynomial Extrapolation n x[n] Estimate Exact Error 1 1.00e-01 1.005012520859400e+00 1.005012520859401e+00 +6.6613e-16 2 2.00e-01 1.020201340026756e+00 1.020201340026756e+00 +0.0000e+00 3 3.00e-01 1.046027859908719e+00 1.046027859908717e+00 -1.9984e-15 4 4.00e-01 1.083287067674962e+00 1.083287067674959e+00 -3.3307e-15 5 5.00e-01 1.133148453066832e+00 1.133148453066826e+00 -5.7732e-15 6 6.00e-01 1.197217363121817e+00 1.197217363121810e+00 -6.8834e-15 7 7.00e-01 1.277621313204896e+00 1.277621313204887e+00 -9.5479e-15 8 8.00e-01 1.377127764335970e+00 1.377127764335957e+00 -1.2657e-14 9 9.00e-01 1.499302500056783e+00 1.499302500056767e+00 -1.5987e-14 10 1.00e+00 1.648721270700146e+00 1.648721270700128e+00 -1.7764e-14 Gragg_Bulirsch_Stoer Method Problem: Solve y' = xy, Initial condition x = 0.0, y = 1.0 Number of steps 10 and step size 0.10 Rational Extrapolation n x[n] Estimate Exact Error 1 1.00e-01 1.005012520859400e+00 1.005012520859401e+00 +6.6613e-16 2 2.00e-01 1.020201340026756e+00 1.020201340026756e+00 +0.0000e+00 3 3.00e-01 1.046027859908719e+00 1.046027859908717e+00 -1.9984e-15 4 4.00e-01 1.083287067674962e+00 1.083287067674959e+00 -3.3307e-15 5 5.00e-01 1.133148453066832e+00 1.133148453066826e+00 -5.7732e-15 6 6.00e-01 1.197217363121817e+00 1.197217363121810e+00 -6.8834e-15 7 7.00e-01 1.277621313204896e+00 1.277621313204887e+00 -9.5479e-15 8 8.00e-01 1.377127764335970e+00 1.377127764335957e+00 -1.2657e-14 9 9.00e-01 1.499302500056783e+00 1.499302500056767e+00 -1.5987e-14 10 1.00e+00 1.648721270700146e+00 1.648721270700128e+00 -1.7764e-14