Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems  

作　　者：Relja Vulanovi 

机构地区：[1]Department of Mathematical Sciences Kent State University Stark Campus

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2008年第2期235-244,共10页高等学校计算数学学报（英文版）

摘　　要：The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L^1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.The paper is concerned with strongly nonlinear singularly perturbed boundary value problems in one dimension. The problems are solved numerically by finite-difference schemes on special meshes which are dense in the boundary layers. The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed. For the central scheme, error estimates are derived in a discrete L^1 norm. They are of second order and decrease together with the perturbation parameter ε. The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically. Numerical results show ε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.

关 键 词：Boundary-value problem singular perturbation finite differences Bakhvalov and piecewise equidistant meshes L^1 stability 

分 类 号：O175.7[理学—数学]