A finite difference method for heat equation in the unbounded domain

摘要

The numerical method of the one-dimensional non-homogeneous heat equation on an unbounded domain is considered. Two exact artificial boundary conditions are applied on two artificial boundaries to limit the original problem onto a bounded computational domain. Then the finite difference method is developed by using the method of the reduction of order for the control equation and artificial boundary conditions. It is proved that the finite difference scheme is stable and convergent with the order 2 in space and order 3/2 in time under an energy norm. A non-homogeneous numerical example demonstrates the unconditional stability and the accuracy of the algorithm.