一类抛物型反应扩散方程奇摄动Robin问题的拟合网格方法的参数一致本质第一order convergence
Parameter uniform essentially first order convergence of a fitted mesh method for a class of parabolic singularly perturbed Robin problem for a system of reaction-diffusion equations
摘要：
本文考虑一类具有初始和Robin边界条件的二阶反应扩散型奇摄动微分方程的线性抛物型方程组.该系统的解$\vec u$的组分表现出带有子层的抛物边界层。本文提出了一种由分片均匀Shishkin网格上的经典有限差分格式组成的数值方法。证明了该方法在时间上是一阶收敛的，在空间变量上是本质一阶收敛的，在最大范数下是一致收敛的
英文摘要：
In this paper, a class of linear parabolic systems of singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The components of the solution $\vec u$ of this system exhibit parabolic boundary layers with sublayers. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first order convergent in time and essentially first order convergent in the space variable in the maximum norm uniformly in the perturbation parameters
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