Higher-order difference and higher-order splitting methods for 2D parabolic problems with mixed derivatives

Abstract

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are higher-order compact alternating direction implicit (ADI) methods. Here we construct a fourth-order splitting method with respect to the weighting factors. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case.