Construction of Implicit–Explicit Second-Derivative BDF Methods

Abstract

In many applications, large systems of ordinary differential equations with both stiff and nonstiff parts have to be solved numerically. Implicit–explicit (IMEX) methods are useful for efficiently solving these problems. In this paper, we construct IMEX second-derivative BDF methods with considerable stability properties. To show the efficiency of the introduced technique, numerical comparisons are given by solving some problems.