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.
Keywords
splitting methods, deferred correction, stability regions
