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Research Paper | Mathematics | India | Volume 12 Issue 5, May 2023 | Popularity: 5 / 10

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Uniform Haar Wavelet Scheme for the Approximate Solution of System of Partially Singularly Perturbed Problems on Non-Uniform Grid

Aditya Sharma, Late Manoj Kumar

Abstract: The purpose of this paper is to present a uniform Haar wavelet method for approximating the solution of a system of partially singularly perturbed problems numerically. The approximate solution is considered on non-uniform grids. Linear and second-order system of partially singularly perturbed problems is considered for different meshes to reduce the issues of singular behavior and provides an approximate solution up to the specified order. By performing the computation on present numerical algorithm, our scheme produces better results than the non-uniform method, the parameter uniform method, and the classical finite difference operator method. The approach is shown to be uniformly convergent in terms of the singular perturbation parameter and error estimation. The effectiveness of the present scheme is examined through some test examples.

Keywords: Differential Equation System, Uniform Haar Wavelet Method, Singular Perturbation, Initial and Boundary Value Problem, Convergence and Error Analysis

Edition: Volume 12 Issue 5, May 2023

Pages: 1165 - 1206

DOI: https://www.doi.org/10.21275/SR23514154953

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