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Numerical simulation of a modified KdV equation on the whole real axis

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Abstract

The numerical simulation of the solution to a modified KdV equation on the whole real axis is considered in this paper. Based on the work of Fokas (Comm Pure Appl Math 58(5):639–670, 2005), a kind of exact nonreflecting boundary conditions which are suitable for numerical purposes are presented with the inverse scattering theory. With these boundary conditions imposed on the artificially introduced boundary points, a reduced problem defined on a finite computational interval is formulated. The discretization of the nonreflecting boundary conditions is studied in detail, and a dual-Petrov–Galerkin spectral method is proposed for the numerical solution to the reduced problem. Some numerical tests are given, which validate the effectiveness, and suggest the stability of the proposed scheme.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Chunxiong Zheng

  2. Institute of Analysis and Scientific Computing, The Vienna University of Technology, Vienna, Austria

    Chunxiong Zheng

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  1. Chunxiong Zheng
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Correspondence to Chunxiong Zheng.

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Supported by the National Natural Science Foundation of China under Grant No. 10401020, the Alexander von Humboldt Foundation, and the Key Project of China High Performance Scientific Computation Research.

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Zheng, C. Numerical simulation of a modified KdV equation on the whole real axis. Numer. Math. 105, 315–335 (2006). https://doi.org/10.1007/s00211-006-0044-z

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  • DOI: https://doi.org/10.1007/s00211-006-0044-z

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