A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0203

W. Lei, Muhammad Ahsan, Waqas Khan, Zaheer Uddin, Masood Ahmad

引用次数: 1

Abstract

Abstract In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference. The nonlinear hyperbolic equation is converted into its full algebraic form once the space derivatives are replaced by the finite Haar series. Convergence analysis is performed both in space and time, where the computational results follow the theoretical statements of convergence. Many test problems with different nonlinear terms are presented to verify the accuracy, capability, and convergence of the proposed method for the first- and second-order nonlinear hyperbolic equations.

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非线性双曲型偏微分方程的数值Haar小波-有限差分混合方法及其收敛性

摘要本文提出了一阶和二阶非线性双曲型方程数值解的Haar小波配点法。控制方程中的时间导数用有限差分近似。将空间导数替换为有限Haar级数，将非线性双曲方程转化为完整的代数形式。在空间和时间上进行了收敛性分析，计算结果符合收敛性的理论表述。为了验证所提方法对一阶和二阶非线性双曲型方程的精度、能力和收敛性，给出了许多不同非线性项的测试问题。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.