具有格林核的第二类Fredholm积分方程的迭代Galerkin解的渐近展开

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Integral Equations and Applications Pub Date : 2020-12-01 DOI:10.1216/jie.2020.32.495

Gobinda Rakshit, Akshay S. Rane

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引用次数: 2

摘要

我们考虑一个具有格林函数型核的第二类Fredholm积分方程。将迭代伽辽金方法应用于这种积分方程。对于r≥1，选择阶≤r−1的分段多项式相对于均匀分区的空间作为近似空间。我们得到了迭代Galerkin解在分区点上的渐近展开式。Richardson外推法用于增加收敛阶数。通过算例说明了我们的理论结果。

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Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green's kernel

We consider a Fredholm integral equation of the second kind with kernel of the type of Green’s function. Iterated Galerkin method is applied to such an integral equation. For r≥1, a space of piecewise polynomials of degree ≤r−1 with respect to a uniform partition is chosen to be the approximating space. We obtain an asymptotic expansion for the iterated Galerkin solution at the partition points. Richardson extrapolation is used to increase the order of convergence. A numerical example is considered to illustrate our theoretical results.

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来源期刊

Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.