Two-Dimensional Uniform and Non-Uniform Haar Wavelet Collocation Approach for a Class of Nonlinear PDEs

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2023-09-30 DOI:10.3390/computation11100189

Narendra Kumar, Amit K. Verma, Ravi P. Agarwal

引用次数: 0

Abstract

In this paper, we introduce a novel approach employing two-dimensional uniform and non-uniform Haar wavelet collocation methods to effectively solve the generalized Burgers–Huxley and Burgers–Fisher equations. The demonstrated method exhibits an impressive quartic convergence rate. Several test problems are presented to exemplify the accuracy and efficiency of this proposed approach. Our results exhibit exceptional accuracy even with a minimal number of spatial divisions. Additionally, we conduct a comparative analysis of our results with existing methods.

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一类非线性偏微分方程的二维均匀与非均匀Haar小波配置方法

本文提出了一种利用二维均匀和非均匀Haar小波配置方法有效求解广义burger - huxley方程和burger - fisher方程的新方法。所证明的方法具有令人印象深刻的四次收敛速度。通过几个测试问题验证了该方法的准确性和有效性。我们的结果即使在最小数量的空间划分下也表现出卓越的准确性。此外，我们将我们的结果与现有方法进行比较分析。

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

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.