Original article: Lanczos-Chebyshev pseudospectral methods for wave-propagation problems

  • Authors:

  • Peter Y. P. Chen;Boris A. Malomed

  • Affiliations:

  • School of Electrical Engineering & Telecommunication, University of New South Wales, Sydney 2052, Australia;Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69979, Israel

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2012

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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 Schrodinger (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.