Scholarlink

<p>New differentiation matrices (DMs) forms have been constructed using the pseudo-spectral method via the second kind of Chebyshev polynomials (SK-CHPs) as basis functions. For that purpose, firstly, we determined the Gauss-Lobatto quadrature points (GLQPs) and weights (GLQWs) concerning SK-CHPs. The newly investigated matrices convert the given initial boundary problem into a system of algebraic equations. The unknowns of the obtained system are the values of the problem’s dependent variables at the calculated GLQPs. In addition, error analysis discussion, and concept for the upper bound of the spectral expansion derivative have been introduced and proved to assess and ensure the correctness of the proposed matrices. Finally, the presented method and the constructed matrices are applied to numerical tests. The numerical simulations are divided into two categories. The first category differentiates known test functions; however, the second category is devoted to approximating the solution to several initial boundary problems for several applications. The obtained results confirm the constructed matrices’ accuracy, consistency, efficiency, and stability.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Pseudo-spectral second kind Chebyshev polynomials differentiation matrices for solving high-order nonlinear differential equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月1日

查看全文
  • Somaya Mahmoud,
  • M. El-Kady,
  • M. Abdelhakem

摘要

New differentiation matrices (DMs) forms have been constructed using the pseudo-spectral method via the second kind of Chebyshev polynomials (SK-CHPs) as basis functions. For that purpose, firstly, we determined the Gauss-Lobatto quadrature points (GLQPs) and weights (GLQWs) concerning SK-CHPs. The newly investigated matrices convert the given initial boundary problem into a system of algebraic equations. The unknowns of the obtained system are the values of the problem’s dependent variables at the calculated GLQPs. In addition, error analysis discussion, and concept for the upper bound of the spectral expansion derivative have been introduced and proved to assess and ensure the correctness of the proposed matrices. Finally, the presented method and the constructed matrices are applied to numerical tests. The numerical simulations are divided into two categories. The first category differentiates known test functions; however, the second category is devoted to approximating the solution to several initial boundary problems for several applications. The obtained results confirm the constructed matrices’ accuracy, consistency, efficiency, and stability.