An A-stable extended trapezoidal rule for the integration of ordinary differential equations

Abstract

We examine a single-step implicit-integration algorithm which is obtained by a modification of the well-known trapezoidal rule. The obtained new method is a third-order numerical process and preserves the property of A-stability of the trapezoidal rule. Numerical examples involving stiff linear systems of first-order differential equations are also included to demonstrate the practical usefulness of this new integration procedure. © 1985.