{"title":"求解三维对流扩散方程的巴利心理性插值法","authors":"Jin Li, Yongling Cheng","doi":"10.1016/j.jat.2024.106106","DOIUrl":null,"url":null,"abstract":"<div><div>Barycentric rational interpolation collocation method (BRICM) is presented to solve 3-dimensional convection–diffusion (CD) equation. The unknown value is approximated by barycentric rational interpolation basis, the discrete CD equation is written into the matrix equation. At last, the stability and convergence rate of BRIM for CD equation are proven and a numerical example is illustrated in our results.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Barycentric rational interpolation method for solving 3 dimensional convection–diffusion equation\",\"authors\":\"Jin Li, Yongling Cheng\",\"doi\":\"10.1016/j.jat.2024.106106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Barycentric rational interpolation collocation method (BRICM) is presented to solve 3-dimensional convection–diffusion (CD) equation. The unknown value is approximated by barycentric rational interpolation basis, the discrete CD equation is written into the matrix equation. At last, the stability and convergence rate of BRIM for CD equation are proven and a numerical example is illustrated in our results.</div></div>\",\"PeriodicalId\":54878,\"journal\":{\"name\":\"Journal of Approximation Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Approximation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021904524000947\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Approximation Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021904524000947","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
提出了用于求解三维对流扩散（CD）方程的重心有理插值法（BRICM）。未知值由重心有理插值基近似，离散 CD 方程被写入矩阵方程。最后，证明了对流扩散方程 BRIM 的稳定性和收敛率，并以数值结果为例进行了说明。
Barycentric rational interpolation method for solving 3 dimensional convection–diffusion equation
Barycentric rational interpolation collocation method (BRICM) is presented to solve 3-dimensional convection–diffusion (CD) equation. The unknown value is approximated by barycentric rational interpolation basis, the discrete CD equation is written into the matrix equation. At last, the stability and convergence rate of BRIM for CD equation are proven and a numerical example is illustrated in our results.
期刊介绍：
The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others:
• Classical approximation
• Abstract approximation
• Constructive approximation
• Degree of approximation
• Fourier expansions
• Interpolation of operators
• General orthogonal systems
• Interpolation and quadratures
• Multivariate approximation
• Orthogonal polynomials
• Padé approximation
• Rational approximation
• Spline functions of one and several variables
• Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds
• Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth)
• Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis
• Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth)
• Gabor (Weyl-Heisenberg) expansions and sampling theory.
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