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Abstract <p>A finite-difference scheme of the predictor–corrector type is constructed for solving nonlinear dispersion equations of wave hydrodynamics with higher order approximation of the dispersion relation for the case of two spatial variables. The numerical algorithm is based on splitting the original system of equations into a hyperbolic system and a scalar equation of the elliptic type. Two methods of approximating the elliptic part are considered. For each of the variants of the difference scheme, dissipation and dispersion analysis is performed, stability conditions are obtained, formulas for the phase error are analyzed, and the behavior of the harmonic attenuation coefficient is studied. A comparative analysis is carried out to identify the advantages of each of the schemes.</p>

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On the Properties of Difference Schemes for Solving Nonlinear Dispersion Equations of Increased Accuracy. II. The Case of Two Spatial Variables

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Z. I. Fedotova,
  • G. S. Khakimzyanov,
  • O. I. Gusev

摘要

Abstract

A finite-difference scheme of the predictor–corrector type is constructed for solving nonlinear dispersion equations of wave hydrodynamics with higher order approximation of the dispersion relation for the case of two spatial variables. The numerical algorithm is based on splitting the original system of equations into a hyperbolic system and a scalar equation of the elliptic type. Two methods of approximating the elliptic part are considered. For each of the variants of the difference scheme, dissipation and dispersion analysis is performed, stability conditions are obtained, formulas for the phase error are analyzed, and the behavior of the harmonic attenuation coefficient is studied. A comparative analysis is carried out to identify the advantages of each of the schemes.