A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation

Abstract

We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractional splitting strategy applied alternately at each intermediate time step to the one dimensional heat equation. As the basis of derivation is the unconditionally stable (4,2) accurate ADI scheme, this method is convergent, computationally stable and highly accurate.