Extended one-step methods for the numerical solution of ordinary differential equations

Abstract

A class of one-step finite difference formulae for the numerical solution of first-order differential equations is considered. The accuracy and stability properties of these methods are investigated. By judicious choice of the coefficients in these formulae a method is derived which is both A-stable and third-order convergent. Moreover the new method is shown to be L-stable and so is appropriate for the solution of certain stiff equations. Numerical results are presented for several test problems.

Keywords:

• One-step methods
• finite difference equations
• ordinary differential equations
• L-stability

C.R. Categories:

• 5.17