Construction of efficient general linear methods for non-stiff differential systems

Abstract

This paper describes the construction of explicit general linear methods in Nordsieck form with inherent quadratic stability and large areas of the stability region. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods with large area of region of absolute stability. Examples of methods with p = q + 1 = s = r and p = q = s = r - 1 up to order 6 are given.