for a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly find accurate numerical solutions for the highly singularly perturbed problems by a simple collocation technique.

中文翻译：

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基于能量Robin边界函数的搭配法求解二阶奇异摄动常微分方程

对于 Robin 型边界条件下的二阶奇异摄动常微分方程 (ODE)，我们开发了一种能量 Robin 边界函数方法 (ERBFM) 来寻找自动满足 Robin 边界条件的解。对于非奇异 ODE，Robin 边界函数由多项式组成，而归一化指数试验函数用于奇异扰动 ODE。ERBFM 还设计用于保存能量，它可以通过简单的搭配技术快速找到高度奇异扰动问题的准确数值解。