{"title":"Redefined fourth order uniform hyperbolic polynomial B-splines based collocation method for solving advection-diffusion equation","authors":"Mansi S. Palav, Vikas H. Pradhan","doi":"10.1016/j.amc.2024.128992","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, uniform hyperbolic polynomial (UHP) B-spline based collocation method is proposed for solving advection-diffusion equation (ADE) numerically. The Von-Neumann's criterion is used to perform stability analysis. It reveals that the proposed scheme is unconditionally stable. The proposed method is implemented on various examples and numerical outcomes which are reported in table. The numerical outcomes are compared with the other methods available in standard literature. The rate of convergence is also calculated numerically which is found to be closed to 2. The numerical investigation reveals that the developed scheme is efficient, accurate and easy to implement. The proposed method is also applied to solve two-dimensional and three-dimensional ADE to demonstrate the efficiency of proposed scheme.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"484 ","pages":"Article 128992"},"PeriodicalIF":3.5000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0096300324004533/pdfft?md5=7a2b3a6a29e0809e9c99a99b5cac312f&pid=1-s2.0-S0096300324004533-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324004533","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In the present paper, uniform hyperbolic polynomial (UHP) B-spline based collocation method is proposed for solving advection-diffusion equation (ADE) numerically. The Von-Neumann's criterion is used to perform stability analysis. It reveals that the proposed scheme is unconditionally stable. The proposed method is implemented on various examples and numerical outcomes which are reported in table. The numerical outcomes are compared with the other methods available in standard literature. The rate of convergence is also calculated numerically which is found to be closed to 2. The numerical investigation reveals that the developed scheme is efficient, accurate and easy to implement. The proposed method is also applied to solve two-dimensional and three-dimensional ADE to demonstrate the efficiency of proposed scheme.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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