The aim of this paper is to develop an accurate symmetric collocation scheme for a class of linear stationary singular perturbation problems with two boundary layers. To adapt to the character of solutions, piecewise reproducing kernels is constructed. In the boundary layers intervals, inverse multiquadrics kernel function is employed. In the regular interval, exponential kernel function is used. On the basis of the piecewise reproducing kernels, a new symmetric collocation technique is presented for the considered linear stationary singular perturbation problems. Results of numerical tests illustrate that our method is easy to implement and is uniformly effective for any small ε.

中文翻译：

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线性平稳奇摄动问题的基于分段分段核的对称配置方法

本文的目的是为一类带有两个边界层的线性平稳奇异摄动问题开发一种精确的对称配置方案。为了适应解决方案的特点，构建了分段复制内核。在边界层间隔中，采用逆多二次核函数。在规则间隔中，使用指数内核函数。在分段再现核的基础上，针对所考虑的线性平稳奇异摄动问题，提出了一种新的对称配置技术。数值测试结果表明，我们的方法易于实现，并且对于任何小的ε均有效。