求解双调和方程的线性重心有理配点法

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2022-01-01 DOI:10.1515/dema-2022-0151

Jin Li

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引用次数: 9

摘要

摘要采用线性重心有理配置方法研究二维双调和边值问题，用重心有理多项式逼近未知函数。利用矩阵形式，将离散双调和方程的线性方程转化为矩阵方程。从重心有理多项式的收敛速度出发，给出了双调和方程线性重心有理配置方法的收敛速度。最后，通过数值算例验证了理论分析的正确性。

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Linear barycentric rational collocation method for solving biharmonic equation

Abstract Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.