关键词: 奇异摄动, 内层, 宽度估计, 有理谱配点法, 区域分解

Abstract:

For solving singular perturbed interior layer problems, a numerical method is proposed to estimate the interior layer width. First, by using the domain decomposition method, the original problem is divided into two parts：the reduced problem and the interior problem. Both problems can be discretized and solved by the rational spectral collocation method in barycentric form. In order to determine the interior layer width, it designs a nonlinear optimization problem based on the continuity condition of first order derivatives. Further, a class of nonlinear interior layer problems is considered and Adomian decomposition method is introduced to deal with the nonlinear term. Numerical results illustrate the feasibility and validity of the proposed numerical method for both linear and nonlinear problems, good accuracy can be obtained when the interior layer width is estimated effectively.

Key words: singular perturbed, interior layer, width estimation, rational spectral collocation method, domain decomposition