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An analysis of the finite-difference method for one-dimensional KleinGordon equation on unbounded domain

Houde Han Zhiwen Zhang

Numerical Analysis and Scientific Computing mathscidoc:1912.431039

Applied Numerical Mathematics, 59, (7), 1568-1583, 2009.7
The numerical solution of the one-dimensional KleinGordon 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 <i>Z</i>-transform approach. Finally, we illustrate the efficiency of the proposed method by several numerical examples.
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@inproceedings{houde2009an,
  title={An analysis of the finite-difference method for one-dimensional KleinGordon equation on unbounded domain},
  author={Houde Han, and Zhiwen Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211417844919603},
  booktitle={Applied Numerical Mathematics},
  volume={59},
  number={7},
  pages={1568-1583},
  year={2009},
}
Houde Han, and Zhiwen Zhang. An analysis of the finite-difference method for one-dimensional KleinGordon equation on unbounded domain. 2009. Vol. 59. In Applied Numerical Mathematics. pp.1568-1583. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211417844919603.
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