奇异摄动问题近似解及其加权误差导数的分析

Error analysis of the approximated solution and derivative for singularly perturbed problems

奇异摄动两点边值问题在均匀网格上得不到稳定可靠的数值解,必须构建自适应网格.此网格是通过等分布在一个区域上的控制函数而产生.针对该类问题,一般的非守恒形式的方程选用对方程二阶导数为向前差商的迎风差分格式以及对控制函数取值为弧长函数的离散形式,利用离散格林函数得到不依赖于摄动参数的收敛结果,近似解的误差阶和加权误差导数的阶均为一阶.

A singularly perturbed two-point boundary value problem with an exponential boundary layer can＇t give a satisfactory numerical solution on an even mesh. It can solved numerically by using an adaptive grid method. The mesh is constructed adaptively by equidistributing a monitor function based on the arc-length of the approximated solution. We choose an upwind difference scheme based on the forward difference approximation for the second-order derivative. By using the discrete Green＇s function, a first-order uniformly convergent result which is independent of the perturbation parameter is obtained. And the error bound for the weighted derivative is also In：st-order uniformly convergent.