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Lanczos–Chebyshev pseudospectral methods for wave-propagation problems

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  • Chen, Peter Y.P.
  • Malomed, Boris A.

Abstract

The pseudospectral approach is a well-established method for studies of the wave propagation in various settings. In this paper, we report that the implementation of the pseudospectral approach can be simplified if power-series expansions are used. There is also an added advantage of an improved computational efficiency. We demonstrate how this approach can be implemented for two-dimensional (2D) models that may include material inhomogeneities. Physically relevant examples, taken from optics, are presented to show that, using collocations at Chebyshev points, the power-series approximation may give very accurate 2D soliton solutions of the nonlinear Schrödinger (NLS) equation. To find highly accurate numerical periodic solutions in models including periodic modulations of material parameters, a real-time evolution method (RTEM) is used. A variant of RTEM is applied to a system involving the copropagation of two pulses with different carrier frequencies, that cannot be easily solved by other existing methods.

Suggested Citation

  • Chen, Peter Y.P. & Malomed, Boris A., 2012. "Lanczos–Chebyshev pseudospectral methods for wave-propagation problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1056-1068.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:6:p:1056-1068
    DOI: 10.1016/j.matcom.2011.05.013
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