Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems. In order to discretize the solution domain, Micken’s type discretization on a uniform mesh is applied and then followed by the fitted operator approach. The convergence of the method is established and observed to be first-order convergent, but it is accelerated by Richardson extrapolation. To validate the applicability of the proposed method, some numerical examples are considered and observed that the numerical results confirm the agreement of the method with the theoretical results effectively. Furthermore, the method is convergent regardless of perturbation parameter and produces more accurate solution than the standard methods for solving singularly perturbed parabolic problems.

中文翻译：

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奇异摄动双参数抛物线对流-扩散问题的稳健有限差分法

为了解决奇异摄动的两个参数抛物线对流扩散问题，引入了稳健的有限差分法。为了对解域进行离散化，在均匀网格上应用 Micken 类型离散化，然后采用拟合算子方法。该方法的收敛性是建立的，并且观察到是一阶收敛的，但通过 Richardson 外推法加速。为了验证所提方法的适用性，考虑并观察了一些数值例子，数值结果有效地证实了该方法与理论结果的一致性。此外，无论扰动参数如何，该方法都是收敛的，并且比求解奇异扰动抛物线问题的标准方法产生更准确的解。