Matrix methods for the forced diffusion equation

Abstract

Finite difference methods for the forced diffusion equation with time dependent boundary conditions are developed using matrices to represent both the approximate solution and the difference operations. This technique allows the boundary conditions to be included in a natural way and eliminates the need for an analysis of the commutativity of the spatial difference operations. The matrix methods are used to develop algorithms that are second order accurate in space and time for a standard square domain and an annular domain.

Keywords:

• Diffusion Equation
• Heat Equation
• Lod
• Adi

C.R. Categories:

• 5.17