Wavelet-based approximation for two-parameter singularly perturbed problems with Robin boundary conditions

Abstract

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.