In this article, we present a highly-accurate wavelet-based approximation to study and analyze the physical and numerical aspects of two-parameter singularly perturbed problems with Robin boundary conditions. To explore the swiftly changing behavior of such problems, we have used a special type of non-uniform mesh known as Shishkin mesh. Using Shishkin mesh with the Haar wavelet scheme contains a novelty in itself. We comprehensively explain an approach to solve the Robin boundary conditions involving the proposed Haar wavelet scheme. Through rigorous analysis, the order of convergence of the present scheme is shown quadratic and linear in the spatial and temporal directions, respectively. The robustness and proficiency of the contributed scheme are conclusively demonstrated with three test examples. Irrespective of the problem’s geometry, the proposed method is highly accurate and very economical.

在本文中，我们提出了一种基于小波的高精度逼近，以研究和分析具有Robin边界条件的两参数奇摄动问题的物理和数值方面。为了探索此类问题的快速变化行为，我们使用了一种称为Shishkin网格的特殊类型的非均匀网格。在Haar小波方案中使用Shishkin网格本身具有新颖性。我们全面解释了一种解决涉及所提出的Haar小波方案的Robin边界条件的方法。通过严格的分析，该方案的收敛顺序分别在空间和时间方向上显示为二次和线性。通过三个测试示例来最终证明该贡献方案的鲁棒性和熟练程度。不管问题的几何形状如何，