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