Heatlet approach to diffusion equation on a semi-infinite region

Abstract

We develop Heatlets, the fundamental solutions of heat equation using wavelets, for numerically solving initial-boundary value problems of one dimensional diffusion equation on a quarter plane. This approach does not invovle the notion of artificial boundary conditions. We present the two scale properties of the heatlets and demonstrate the applicability of the heatlet approach by using them in the construction of numerical solution of diffusion equation on a semi-infinite region. The numerical results obtained are compared with those obtained using finite difference and finite element methods that use artificial boundary conditions.