A Meshfree Method for Korteweg-de Vries (KdV) Equation by A New Multiquadric Quasi-interpolation

被引：0

作者：

Xiao, Hualin ^{[1
]}

Qu, Dan ^{[1
]}

机构：

[1] College of Mathematics Education, China West Normal University, Sichuan, Nanchong,637009, China

来源：

IAENG International Journal of Applied Mathematics | 2024年 / 54卷 / 06期

关键词：

Computational mechanics - Interpolation - Korteweg-de Vries equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The quasi-interpolation operator is widely used in numerical approximation and numerical solutions of differential equations. This paper proposes a new multiquadric(MQ) quasi-interpolate and formulates a meshfree method for the Korteweg-de Vries(KdV) equation based on the proposed multiquadric quasi-interpolate. More specifically, based on the multiquadric function, a new univariate multiquadric(MQ) quasi-interpolation scheme is structured, which possesses high accuracy, simple structure, and ease of programming. Moreover, the error estimation of the new quasi-interpolate is shown in detail. Next, a meshfree method for the Korteweg-de Vries (KdV) is proposed by using the novel multiquadric(MQ) quasi-interpolation operator. In the spatial direction, the derivative is approximated by the proposed multiquadric quasi-interpolate, and the forward divided difference approximates the temporal derivative. Several numerical examples are presented at the end of the paper to verify the expected approximation capability, and the experiment results show that the meshfree method (based on the new multiquadric(MQ) quasi-interpolation operator) is valid. © (2024), (International Association of Engineers). All Rights Reserved.

引用

页码：1172 / 1181