New extrapolation methods for initial value problems in ordinary differential equations

Abstract

In Ikhile (1998), a family of variable order inverse nonlinear rational methods for which the inverse-Euler is a special case has been developed. This present consideration examines the extrapolation of this class of methods. In fact, we show that in the limit of increasing order, the extrapolation of the generalised class of methods remain highly stable. In particular, the L-stability of the inverse Euler remains a preserved property after polynomial extrapolation. The accuracy of the numerical results from extrapolation based on these methods appear quite overwhelming when compared to results from DIFEX2 of Fatunla (1986,1988), DIFEX1 of Deuflhard (1983) and GBS extrapolation method of Gragg (1965) and Bulirsch and Stoer (1966).

Keywords:

• Extrapolation
• Rational
• Variable
• Order
• Stability

C.R. Categories:

• G.17

^∗Corresponding author

^∗Corresponding author

Notes

^∗Corresponding author