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Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems

Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems This paper deals with eigenvalue problems for linear Fredholm integral equations of the second kind with weakly singular kernels. A new discrete method is proposed for the approximation of eigenvalues. Compactness of the integral operator in L 1[0, 1] space is obtained. This method is based on the approximation of the integral operator by modified interpolatory projection. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Further, convergence of eigenvalue approximation is obtained by analytical tools. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems

Acta Mathematicae Applicatae Sinica , Volume 35 (2) – May 15, 2019

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Publisher
Springer Journals
Copyright
Copyright © 2019 by The Editorial Office of AMAS & Springer-Verlag GmbH Germany
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-019-0823-9
Publisher site
See Article on Publisher Site

Abstract

This paper deals with eigenvalue problems for linear Fredholm integral equations of the second kind with weakly singular kernels. A new discrete method is proposed for the approximation of eigenvalues. Compactness of the integral operator in L 1[0, 1] space is obtained. This method is based on the approximation of the integral operator by modified interpolatory projection. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Further, convergence of eigenvalue approximation is obtained by analytical tools. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: May 15, 2019

References