Extended a-stable two-step methods for the numerical solution of ordinary differential equations

Abstract

A class of two-step finite difference formulae for the numerical solution of first order differential equations is investigated. A particular one parameter family of methods is derived which is shown to be fourth order convergent and A-stable. Numerical results are presented for several test problems.

Keywords:

• Two-step methods
• finite difference methods
• ordinary differential equations
• A-stability

C.R. Category:

• G.17