Sixth-Order Stable Implicit Finite Difference Scheme for 2-D Heat Conduction Equation on Uniform Cartesian Grids with Dirichlet Boundaries

Abstract

Constructing higher-order difference schemes are always challenging for boundary value problems. The core part is to define boundary enclosure in such a way that guarantees stability and uniform order of accuracy for all nodes. In this work, we develop sixth-order implicit finite difference scheme for 2-D heat conduction equation with Dirichlet boundary conditions. The computed generalized eigenvalues of implicit finite difference matrices have negative real parts that guarantees stability in the case of Crank-Nicolson method. The validity of our developed numerical scheme is clearly reflected by the numerical testing