Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems. Issue 3 (June 2014)

• Record Type: Journal Article
• Authors: Han, Houde; Shih, Yin-Tzer; Tsai, Chih-Ching
• Is Part Of: Advances in applied mathematics and mechanics. Volume 6:Issue 3(2014)
• Page Start: 376
• Page End: 402
• Publication Date: 2014-06
• Subjects: 65N25, -- 35B25, -- 74G15, -- 81Q05; Singular perturbation, -- tailored finite point, -- Schrödinger equation, -- eigenvalue problem; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2013.m376
• Languages: English
• ISSNs: 2070-0733

Abstract

Abstract: We propose two variants of tailored finite point (TFP) methods for discretizing two dimensional singular perturbed eigenvalue (SPE) problems. A continuation method and an iterative method are exploited for solving discretized systems of equations to obtain the eigen-pairs of the SPE. We study the analytical solutions of two special cases of the SPE, and provide an asymptotic analysis for the solutions. The theoretical results are verified in the numerical experiments. The numerical results demonstrate that the proposed schemes effectively resolve the delta function like of the eigenfunctions on relatively coarse grid.