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首页> 外文会议>Bail 2008 - boundary and interior layers >A Parameter-Uniform Finite Difference Method for a Singularly Perturbed Initial Value Problem: A Special Case
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A Parameter-Uniform Finite Difference Method for a Singularly Perturbed Initial Value Problem: A Special Case

机译：奇异摄动初值问题的参数一致有限差分方法：一种特殊情况

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摘要

A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be distinct. The components of the solution exhibit overlapping layers. A Shishkin piecewise-uniform mesh is constructed, which is used, in conjunction with a classical finite difference discretisation, to form a new numerical method for solving this problem. It is proved, in a special case, that the numerical approximations obtained from this method are essentially first order convergent uniformly in all of the parameters. Numerical results are presented in support of the theory.
机译：考虑具有给定初始条件的一阶奇异摄动常微分方程组。每个方程的前导项乘以一个小的正参数。假定这些参数是不同的。溶液的组分具有重叠的层。构造了Shishkin分段均匀网格，将其与经典的有限差分离散化结合使用，以形成解决该问题的新数值方法。证明在特殊情况下，从该方法获得的数值近似值在所有参数上基本上都是一阶收敛的。数值结果为理论提供了支持。

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