A class of artificial boundary conditions for heat equation in unbounded domains

In this paper, the numerical solutions of three problems of heat equation on unbounded domains are considered. For each problem, we introduce an artificial boundary Γ to make the computational domain finite. On the artificial boundary Γ, we propose an exact artificial boundary condition to reduce the original problem to an initial-boundary problem of heat equation on the finite computational domain, which is equivalent to the original problem. Then the finite difference method and finite element method are used to solve the reduced problem on the finite computational domain. In the end of this paper, three numerical examples show the feasibility and effectiveness of the method given in this paper.