Title: Asymptotic expansions for approximate eigenvalues of integral operators with a weakly singular periodic kernel

Authors: Rekha P. Kulkarni; Akshay S. Rane

Addresses: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India ' Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

Abstract: We consider the approximation of an eigenvalue of an integral operator with a weakly singular periodic kernel using the modified Nyström scheme based on the composite trapezoidal rule. Numerical results are presented which confirm the theoretical orders of convergence.

Keywords: asymptotic expansion; modified Nystrom scheme; weakly singular periodic kernel; approximate eigenvalues; integral operators; composite trapezoidal rule.

DOI: 10.1504/IJCONVC.2016.080402

International Journal of Convergence Computing, 2016 Vol.2 No.1, pp.79 - 92

Received: 14 Apr 2015
Accepted: 16 Jun 2016
Published online: 21 Nov 2016 *