Exact non-reflecting boundary conditions
Journal of Computational Physics
Fast adaptive methods for the free-space heat equation
SIAM Journal on Scientific Computing
Artificial boundary method for two-dimensional Burgers' equation
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
A local high-order doubly asymptotic open boundary for diffusion in a semi-infinite layer
Journal of Computational Physics
Artificial Boundary Conditions for the Simulation of the Heat Equation in an Infinite Domain
SIAM Journal on Scientific Computing
Numerical solution of the heat equation in unbounded domains using quasi-uniform grids
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Computation of some unsteady flows over porous semi-infinite flat surface
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Journal of Computational Physics
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The finite difference solution of one-dimensional heat conduction equation in unbounded domains is considered. An artificial boundary is introduced to make the computational domain finite. On the artificial boundary an exact boundary condition is applied to reduce the original problem to an initial-boundary value problem. A finite difference scheme is constructed by the method of reduction of order. It is proved that the finite difference scheme is uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time under an energy norm. A numerical example demonstrates the theoretical results.