Numerical Analysis for a weakly coupled system of Singularly Perturbed Quasilinear Problem with non-smooth data

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

Journal of Computational Science Pub Date : 2025-02-01 DOI:10.1016/j.jocs.2024.102475

Ruby , Vembu Shanthi , Higinio Ramos

引用次数: 0

Abstract

This paper aims at solving a weakly coupled system of quasilinear convection diffusion equations with jump discontinuities in the convection and source terms. Due to the presence of a jump discontinuity in the convection term, the solution exhibits strong interior layers at the point of discontinuity. To approximate the solution of this problem, a hybrid difference technique is used and implemented on a Shishkin mesh. The proposed technique is proven to present an almost second order uniform convergence. To validate the theoretical results, some numerical examples are presented.

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一类具有非光滑数据的弱耦合奇摄动拟线性问题的数值分析

本文的目的是求解一类弱耦合的准线性对流扩散方程组，该方程组的对流项和源项具有跳变不连续。由于对流项存在跳跃不连续，溶液在不连续点处呈现出很强的内层。为了逼近这一问题的解，采用了一种混合差分技术，并在Shishkin网格上实现。结果表明，该方法具有近似二阶一致收敛性。为了验证理论结果，给出了一些数值算例。

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).