A Class of Exponential Integrators Based on Spectral Deferred Correction

Abstract

This paper introduces a new class of exponential integrators based on spectral deferred correction. These new methods are simple to implement at any order of accuracy and can be used to efficiently solve initial value problems when high precision is desired. We begin by deriving exponential spectral deferred correction (ESDC) methods for solving both partitioned and unpartitioned initial value problems. We then analyze the linear stability properties of these new integrators and show that they are comparable to those of existing semi-implicit spectral deferred correction schemes. Finally, we present five numerical experiments to demonstrate the improved efficiency of our new exponential integrator compared to semi-implicit spectral deferred correction schemes and existing fourth-order exponential Runge--Kutta methods.