Efficient eighth order p-stable methods for second order initial value problems

Abstract

A family of eighth order P-stable methods for solving second order initial value problems is considered. The nonlinear algebraic systems, which results on applying one of the methods in this family to a nonlinear differential system, may be solved by using a modified Newton method. We derive methods which require only four (new) function evaluations per iteration and for which the iteration matrix is a true real perfect quartic. This means that at most one real matrix must be factorised at each step. Finally numerical results are presented to illustrate our local error estimation technique.

Keywords:

• P stable method
• 2^nd order I.V. problem
• modified Newton method

C.R.Categories:

• G.1.7