On the spectral deferred correction of splitting methods for initial value problems

Abstract

Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full accuracy of the underlying quadrature rule is attainable. We also examine experimentally the stability properties of the methods for various splittings of advection-diffusion and reaction-diffusion equations.