Numerical Solutions of Parabolic Problems on Unbounded 3-D Spatial Domain (Journal of Computational Mathematics, 2005)
In this paper, the numerical solutions of heat equation on 3-D unbounded spatial domain are considered. An artificial boundary $Γ$ is introduced to finite the computational domain. On the artificial boundary $Γ$, the exact boundary condition and a series of approximating boundary conditions are derived, which are called artificial boundary conditions. By the exact or approximating boundary condition on the artificial boundary, the original problem is reduced to an initial-boundary value problem on the bounded computational domain, which is equivalent or approximating to the original problem. The finite difference method and finite element method are used to solve the reduced problems on the finite computational domain. The numerical results demonstrate that the method given in this paper is effective and feasible.