Open Access Research

Computing eigenvalues and Hermite interpolation for Dirac systems with eigenparameter in boundary conditions

Mohammed M Tharwat

Author Affiliations

Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

Boundary Value Problems 2013, 2013:36  doi:10.1186/1687-2770-2013-36

Published: 21 February 2013


Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper we use the derivative sampling theorem ‘Hermite interpolations’ to compute approximate values of the eigenvalues of Dirac systems with eigenvalue parameter in one or two boundary conditions. We use recently derived estimates for the truncation and amplitude errors to compute error bounds. Using computable error bounds, we obtain eigenvalue enclosures. Examples with tables and illustrative figures are given. Also numerical examples, which are given at the end of the paper, give comparisons with the classical sinc-method in Annaby and Tharwat (BIT Numer. Math. 47:699-713, 2007) and explain that the Hermite interpolations method gives remarkably better results.

MSC: 34L16, 94A20, 65L15.

Dirac systems; eigenvalue problems with eigenparameter in the boundary conditions; Hermite interpolations; truncation error; amplitude error; sinc methods