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

摘要

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