Mathematics

CLC number: O242

The Space-Time Semi-Analytical Meshless Methods for Coupled Burgers' Equations

耦合Burgers方程的时空半解析无网格方法

¹ College of Architectural Engineering, Zhengzhou Business University, Zhengzhou 451200, Henan, China
² Institute of Data Science and Engineering, Xuzhou University of Technology, Xuzhou 221018, Jiangsu, China

^† Corresponding author. E-mail: wangfuzhang1984@163.com

Received: 25 January 2024

Abstract

In this paper, a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers' equations. During the whole solution procedure, two different schemes are considered in terms of radial and non-radial basis functions. The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an "isotropic" space-time radial basis function. The second non-radial scheme considered relationship between time-dependent and space-dependent variables. Under such circumstance, we can get a one-step space-time meshless scheme. The numerical findings demonstrate that the proposed meshless schemes are precise, user-friendly, and effective in solving the coupled Burgers' equations.

摘要

本文提出了一种简单的半解析直接时空无网格格式用于耦合Burgers方程的数值近似求解。在求解过程中，考虑了径向基函数和非径向基函数两种不同的方案。第一种径向基函数方案中的时间相关变量被直接视为正常空间变量，进而给出了“各向同性”时空径向基函数；第二种非径向基函数方案考虑了时间相关和空间相关变量之间的关系。在这种情况下，我们可以得到一种一步式时空无网格方案。数值结果表明，所提出的无网格方法精度良好、使用友好，并能有效地求解耦合的Burgers方程。