Extrapolated Implicit–Explicit Runge–Kutta Methods

Abstract

We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by stage values in the previous step. This approach was first proposed by the authors in context of implicit–explicit general linear methods.

Keywords

• non-stiff and stiff processes
• extrapolated IMEX methods
• Runge–Kutta methods
• error and stability analysis
• construction of highly stable methods