Numerical Solution of the Diffusion Equation by a Potential Method

The main advantage of using potential methods for generating numerical solutions to elliptic partial differential equations is that the dimension of the problem is reduced by one. This feature reduces, not only the number of algebraic equations to be solved, but also alleviates the problems of mesh generation. Both of these factors combine to reduce considerably the cost of computing acceptable numerical solutions. In this paper a potential method is developed which essentially extends to the diffusion equation most of the advantages currently afforded to elliptic equations.