Lanczos–Chebyshev pseudospectral methods for wave-propagation problems

Peter Y.P. Chen and Boris A. Malomed

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 6, 1056-1068

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.

Keywords: Pseudospectral Chebyshev method; Nonlinear Schrödinger equations; Waves in complex media; Solitary wave propagation; Real-time evolution method (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:6:p:1056-1068

DOI: 10.1016/j.matcom.2011.05.013

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