【摘要】 考虑奇异摄动反应扩散方程,这是一个多尺度问题,问题在左右两边皆产生边界层现象.根据边界层的奇性,提出不等距的有限差分格式,其主要思想是根据Shishkin过渡点将区域分为边界层区域和边界层外区域,在边界层外采用等距的大步长,在边界层区域内逐步增加网格步长.有一半的网格步长是不同的.进行了截断误差估计。并证明所提方法是稳定的,一致收敛性高于2阶.最后给出数值例子以说明理论结果的正确性.更多还原

【Abstract】 Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is con- sidered.This is a multi-scale problem.The presence of small parameter leads to boundary laver phe- nomena on both sides of region.Non-equidistant finite difference method was presented according to the property of boundary layer.The region was divided into the inner boundary layer region and the outside boundary layer region according to transition point of Shishkin.The step length is equidistant on the outside boundary layer region.The step length is gradually increased on the inner boundary layer region such that half of the step length is different from each other.Truncation error was esti- mated.The new method is stable and uniform convergence with order higher than 2.Finally,numeri- cal results were given,which are in agreement with the theoretical result.更多还原