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 discreti...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.展开更多
基金the National Natural Science Foundation of China through NSFC No.11371218 and No.91330203the second author was supported by the National Science Council of Taiwan through NSC 102-2115-M005-005.
文摘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.
