On the Properties of Difference Schemes for Solving Nonlinear Dispersive Equations of Increased Accuracy. I. The Case of One Spatial Variable

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2023-12-07 DOI:10.1134/s1995423923040080

Z. I. Fedotova, G. S. Khakimzyanov

引用次数: 0

Abstract

A difference scheme of the predictor–corrector type is constructed for solving nonlinear dispersive equations of wave hydrodynamics with an increased order of approximation of the dispersion relation, based on splitting of the original system of equations into a hyperbolic system and a scalar equation of the elliptic type. A dissipation and dispersion analysis of the new scheme is performed, a condition for its stability is obtained, and a formula for the phase error is written and analyzed. Parameters are found at which the phase characteristics of the difference scheme, the nonlinear-dispersive model approximated by it, and the full model of potential flows have the same order of accuracy.

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论提高非线性分散方程求解精度的差分方案的特性。I. 单空间变量情况

摘要在将原方程系统拆分为双曲系统和椭圆型标量方程的基础上，构建了一种预测器-校正器类型的差分方案，用于求解非线性波流体力学色散方程，并提高了色散关系的近似阶数。对新方案进行了耗散和频散分析，获得了其稳定性条件，并编写和分析了相位误差公式。找到了差分方案的相位特性、其近似的非线性色散模型和完整的势流模型具有相同精度的参数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

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期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.