{"title":"二维耦合Burgers方程的修正三次三角b样条微分积分法数值逼近","authors":"Mamta Kapoor, V. Joshi","doi":"10.2478/ijame-2022-0037","DOIUrl":null,"url":null,"abstract":"Abstract In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between L2 and L∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"84 1","pages":"79 - 102"},"PeriodicalIF":0.0000,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method\",\"authors\":\"Mamta Kapoor, V. Joshi\",\"doi\":\"10.2478/ijame-2022-0037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between L2 and L∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature.\",\"PeriodicalId\":37871,\"journal\":{\"name\":\"International Journal of Applied Mechanics and Engineering\",\"volume\":\"84 1\",\"pages\":\"79 - 102\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Applied Mechanics and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/ijame-2022-0037\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Chemical Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mechanics and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/ijame-2022-0037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Chemical Engineering","Score":null,"Total":0}
A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method
Abstract In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between L2 and L∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature.
期刊介绍：
INTERNATIONAL JOURNAL OF APPLIED MECHANICS AND ENGINEERING is an archival journal which aims to publish high quality original papers. These should encompass the best fundamental and applied science with an emphasis on their application to the highest engineering practice. The scope includes all aspects of science and engineering which have relevance to: biomechanics, elasticity, plasticity, vibrations, mechanics of structures, mechatronics, plates & shells, magnetohydrodynamics, rheology, thermodynamics, tribology, fluid dynamics.
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