Some new methods for stiff differential equations

Abstract

A numerical method applied to the differential equation y′=λy can lead to a solution of the form , where z and w = λh satisfy an equation P(w, z) = 0. In general P(w,z) is a polynomial in both w and z, of degree M in w and N in z. Existing multistep and Runge-Kuta methods correspond to the cases M = 1 and N = 1 respectively. New methods are fottd by taking MS≧2N≧2. The approach here is first to find a suitable polynomial P(w,z) with the desired stability properties, and then to find a process which leads to this polynomial. Third- and fourth-order A- and L-stable processes are given of the semi-explicit arid linearly implicit types.

Keywords:

• Stiff differential equations
• A-stable
• L-stable

C.R. Categories:

• 5.17