抛物型偏微分方程奇异摄动问题的边界层方法

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The Boundary Layer Method for the Solution of Singular Perturbation Problem for the Parabolic Partial Differential Equation

摘要: 本文讨论抛物型偏微分方程奇异摄动问题,通常,为了使边界层的特性不致丧失,在边界层附近必须减小网格,当网格足够小时需要很大的运算量。我们提出边界层格式,在边界层附近不必取很细的网格,数值例子表明采用中等步长即可满足精度。

Abstract: In this paper,we discuss the singular perturbation problem of the parabolic partial differential equation.As usual,we must reduce the mesh size in the neighbourhood of the boundary layer so that typical feature of the boundary layer will not be lost.Then we need very large operational quantity when mesh sizes are getting too small.Now we propose the boundary layer scheme,which need not take very fine mesh size in the neighbourhood of the boundary layer.Numerical examples show that the accuracy can be satisfied with moderate step size.

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