Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems (Advances in Applied Mathematics and Mechanics, 2014)
We propose two variants of tailored finite point (TFP) methods for discretizing two dimensional singular perturbed eigenvalue (SPE) problems. A continuationmethod 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 twospecial cases of the SPE, and provide an asymptotic analysis for the solutions. Thetheoretical results are verified in the numerical experiments. The numerical resultsdemonstrate that the proposed schemes effectively resolve the delta function like ofthe eigenfunctions on relatively coarse grid.