Heatlet approach to diffusion equation on unbounded domains

We develop Heatlets, the fundamental solutions of heat equation using wavelets, for numerically solving inhomogeneous and homogeneous initial value problems of diffusion equation on unbounded domains. Unlike finite difference and finite element methods, diffusion into an infinite medium is satisfied analytically, avoiding the need for artificial boundary conditions on a finite computational domain. The approach is applied to a number of examples and the numerical results confirm the theoretical findings.