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Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems

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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 L1[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.

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Authors and Affiliations

  1. Department of Basic Courses, Beijing Union University, Beijing, 100101, China

    Xin Zhang

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St.John’s, A1C 5S7, Canada

    Yun-hui He

Authors
  1. Xin Zhang
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  2. Yun-hui He
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Correspondence to Xin Zhang.

Additional information

Supported by Scientific Research Project of Beijing Municipal Education Commission (No. KM201811417013, KM201711417002).

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Zhang, X., He, Yh. Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems. Acta Math. Appl. Sin. Engl. Ser. 35, 327–339 (2019). https://doi.org/10.1007/s10255-019-0823-9

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  • DOI: https://doi.org/10.1007/s10255-019-0823-9

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