Numerical Method For Several Singularly Perturbed Problems

Singular perturbation problems appear in many branches of applied math-ematics,and for more than two decades quite a good number of research works on the qualitative and quantitative analysis of these problems for both ordinary differential equations and partial differential equations have been reported in the literature.Most of the papers connected with computational aspects are confined to second order equations.Only few results are reported for higher order equa-tions.In this paper,we present an efficient numerical algorithm for solving a class of singularly perturbed fourth order equations.This method is based on Max-imum principle by the coefficient's asymptotic expansion decompose the fourth order equations into a singularly perturbed second order equation and a second order ordinary differential equation.Then,we use the Maximum principle ob-tain the error estimate between the exact solution and approximate solution. Furthermore,we use the finite element method to solve the singularly perturbed second order ordinary differential equations.Lastly, we use expansion to discuss a novel method for a class of singularly perturbed second order ordinary differential equations.