连续函数加权空间中volterra积分方程的投影方法

IF 0.9 4区数学 Q2 MATHEMATICS Journal of Integral Equations and Applications Pub Date : 2022-12-01 DOI:10.1216/jie.2022.34.433

T. Diogo, L. Fermo, D. Occorsio

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引用次数: 2

摘要

摘要。本文研究了第二类Volterra积分方程的数值处理，该方程的被积函数具有对角和/或端点代数奇异性。在具有上确界范数的加权连续函数空间中，提出了一种基于最优插值算子的投影方法。在这样的空间中，讨论了解的唯一性，并确定了适当的条件来保证方法的稳定性和收敛性。几个数值试验表明了该方法的有效性以及与理论估计的一致性。

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A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS

A BSTRACT . This paper is concerned with the numerical treatment of second kind Volterra integral equations whose integrands present diagonal and/or endpoint algebraic singularities. A projection method based on an optimal interpolating operator is developed in the spaces of weighted continuous functions endowed with the supremum norm. In such spaces, the uniqueness of the solution is discussed and suitable conditions are determined to assure the stability and the convergence of the method. Several numerical tests are presented to show the efﬁciency of the method and the agreement with the theoretical estimates.

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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.