A Family of Stiffly Stable Second Derivative Block Methods for Initial Value Problems in Ordinary Differential Equations

Abstract

In this paper, we present a family of stiffly stable second derivative block methods (SDBMs) suitable for solving first-order stiff ordinary differential equations (ODEs). The methods proposed herein are consistent and zero stable, hence, they are convergent. Furthermore, we investigate the local truncation error and the region of absolute stability of the SDBMs. A flowchart, describing this procedure is illustrated. Some of the developed schemes are shown to be A-stable and L-stable, while some are found to be A()-stable. The numerical results show that our SDBMs are stiffly stable and give better approximations than the existing methods in the literature.