Volume 6, Issue 3
Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems

Houde Han ,  Yin-Tzer Shih and Chih-Ching Tsai

10.4208/aamm.2013.m376

Adv. Appl. Math. Mech., 6 (2014), pp. 376-402.

Preview Full PDF BiBTex 1 220
  • 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.

  • History

Published online: 2014-06

  • Cited by