Semi-analytical Approximation for Solving High-order Sturm-Liouville Problems
A. H. S. Taher *
Department of Mathematics, University of Aden, P.O. Box: 205, Al-Habilain, Aden, Yemen.
A. Malek
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box: 14115-134, Tehran, Iran.
A. S. A. Thabet
Department of Mathematics, University of Aden, P.O. Box: 205, Al-Habilain, Aden, Yemen.
*Author to whom correspondence should be addressed.
Abstract
In this paper, an algorithm for solving high-order non-singular Sturm-Liouville eigenvalue problems is proposed. A modified form of Adomian decomposition method is implemented to provide a semianalytical solution in the form of a rapidly convergent series. Convergent analysis and error estimate based on the Banach fixed-point is discussed. Five high-order Sturm-Liouville problems are solved numerically. Numerical results demonstrate reliability and efficiency of the proposed scheme.
Keywords: High-order Sturm-Liouville problems, Modified Adomian decomposition method, Banach fixed point theorem; Eigenvalues, Eigenfunctions.