In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution to this class of turning point problem possesses two outflow exponential boundary layers. Parameter-explicit theoretical bounds on the analytical solution derivatives are given, which are used in the error analysis of the proposed scheme. A hybrid finite difference scheme discretizes the problem comprising of midpoint-upwind and central difference operator on an appropriate piecewise-uniform fitted mesh. An error analysis has been carried out for the proposed scheme by splitting the solution into regular and singular components, and the method has been shown to be second-order uniformly convergent except for a logarithmic factor with respect to the singular perturbation parameter. Some relevant numerical examples are also illustrated to verify the theoretical aspects computationally. Numerical experiments show that the proposed method gives competitive results compared to those of other methods available in the literature.

本文针对一类奇异摄动的内部转折点问题，构造并分析了参数均匀拟合网格有限差分格式。此类转折点问题的解具有两个流出指数边界层。给出了解析解导数的参数显式理论界限，用于所提出方案的误差分析。混合有限差分方案在适当的分段均匀拟合网格上将包含中点迎风和中心差分算子的问题离散化。通过将解分成规则分量和奇异分量，对所提出的方案进行了误差分析，并且该方法已被证明是二阶一致收敛的，除了关于奇异扰动参数的对数因子。还说明了一些相关的数值例子，以在计算上验证理论方面。数值实验表明，与文献中可用的其他方法相比，所提出的方法给出了有竞争力的结果。