An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain. (English) Zbl 1162.65377
Summary: The numerical solution of the one-dimensional Klein-Gordon equation on an unbounded domain is analyzed in this paper. Two artificial boundary conditions are obtained to reduce the original problem to an initial boundary value problem on a bounded computational domain, which is discretized by an explicit difference scheme. The stability and convergence of the scheme are analyzed by the energy method. A fast algorithm is obtained to reduce the computational cost and a discrete artificial boundary condition (DABC) is derived by the \(Z\)-transform approach. Finally, we illustrate the efficiency of the proposed method by several numerical examples.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
artificial boundary condition (ABC); unbounded domain; energy method; fast algorithm; discrete artificial boundary condition (DABC)References:
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