{"title":"Numerical Analysis for a weakly coupled system of Singularly Perturbed Quasilinear Problem with non-smooth data","authors":"Ruby , Vembu Shanthi , Higinio Ramos","doi":"10.1016/j.jocs.2024.102475","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"85 ","pages":"Article 102475"},"PeriodicalIF":3.1000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1877750324002680","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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.
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).
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