A feasible numerical computation based on matrix operations and collocation points to solve linear system of partial differential equations

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science Pub Date : 2024-09-17 DOI:10.1016/j.jocs.2024.102445

引用次数: 0

Abstract

In this work, a system of linear partial differential equations with constant and variable coefficients via Cauchy conditions is handled by applying the numerical algorithm based on operational matrices and equally-spaced collocation points. To demonstrate the applicability and efficiency of the method, four illustrative examples are tested along with absolute error, maximum absolute error, RMS error, and CPU times. The approximate solutions are compared with the analytical solutions and other numerical results in literature. The obtained numerical results are scrutinized by means of tables and graphics. These comparisons show accuracy and productivity of our method for the linear systems of partial differential equations. Besides, an algorithm is described that summarizes the formulation of the presented method. This algorithm can be adapted to well-known computer programs.

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基于矩阵运算和配位点的可行数值计算，用于求解线性偏微分方程系

在这项工作中，通过柯西条件，应用基于运算矩阵和等间距配置点的数值算法，处理了一个具有常数和可变系数的线性偏微分方程系统。为了证明该方法的适用性和效率，对四个示例进行了绝对误差、最大绝对误差、均方根误差和 CPU 时间的测试。近似解与分析解以及文献中的其他数值结果进行了比较。通过表格和图形对所获得的数值结果进行了仔细检查。这些比较显示了我们的方法对线性偏微分方程系统的准确性和效率。此外，还介绍了一种算法，该算法总结了所介绍方法的表述。该算法可适用于著名的计算机程序。

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

Journal of Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS

CiteScore

5.50

自引率

3.00%

发文量

227

审稿时长

41 days

期刊介绍： Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory. The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation. This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods. Computational science typically unifies three distinct elements: • Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous); • Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems; • Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).