七阶逼近样条在Fredholm周奇点积分方程解中的应用

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-06-28 DOI:10.37394/23206.2023.22.53

I. Burova, G. O. Alcybeev

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引用次数: 0

摘要

利用七阶近似的多项式样条近似构造了具有周奇点的第二类Fredholm积分方程的数值解。七阶近似基样条的支撑占据七个网格间隔。在积分区间的开始、中间和结束时，我们对七阶近似的基样条进行各种修改。我们用高斯型正交公式计算了弱奇点的积分。假定积分方程的解是足够光滑的。采用七阶近似样条的优点是使用较少的网格节点即可达到所需的近似误差。给出了应用七阶样条近似求解积分方程的数值实例。

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Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity

We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order to solve integral equations are given.

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.