Approximation of a System of Singularly Perturbed Reaction—Diffusion Parabolic Equations in a Rectangle

摘要

The Dirichlet problem for a system of singularly perturbed reaction–diffusion parabolicequations in a rectangle is considered. The higher order derivatives of the equations are multiplied by aperturbation parameter c2, where e takes arbitrary values in the interval (0, 1]. When ￡ vanishes, the sys-tem of parabolic equations degenerates into a system of ordinary differential equations with respect tot. When c tends to zero, a parabolic boundary layer with a characteristic width c appears in a neighbor-hood of the boundary. Using the condensing grid technique and the classical finite difference approxi-mations of the boundary value problem, a special difference scheme is constructed that converges c-uni- formly at a rate of O(N~(-2)In~2N + N_0~(-1) ), whereN =minN_s, N_s+ 1 and N_0 + 1 are the numbers of meshpoints on the axes x_s andt,respectively.