Parameter Uniform Numerical Method for a Weakly Coupled System of Second Order Singularly Perturbed Turning Point Problem with Robin Boundary Conditions

Geetha, N.; Tamilselvan, A.

doi:10.1016/j.proeng.2015.11.363

Procedia Engineering

2015

DOI: 10.1016/j.proeng.2015.11.363

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Parameter Uniform Numerical Method for a Weakly Coupled System of Second Order Singularly Perturbed Turning Point Problem with Robin Boundary Conditions

N. Geetha

A. Tamilselvan

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2024

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Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions

Ahmed

2024

J Nonlinear Math Phys

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This paper’s major goal is to provide a numerical approach for estimating solutions to a coupled system of convection–diffusion equations with Robin boundary conditions (RBCs). We devised a novel method that used four homogeneous RBCs to generate basis functions using generalized shifted Legendre polynomials (GSLPs) that satisfy these RBCs. We provide new operational matrices for the derivatives of the developed polynomials. The collocation approach and these operational matrices are utilized to find approximate solutions for the system under consideration. The given system subject to RBCs is turned into a set of algebraic equations that can be solved using any suitable numerical approach utilizing this technique. Theoretical convergence and error estimates are investigated. In conclusion, we provide three illustrative examples to demonstrate the practical implementation of the theoretical study we have just presented, highlighting the validity, usefulness, and applicability of the developed approach. The computed numerical results are compared to those obtained by other approaches. The methodology used in this study demonstrates a high level of concordance between approximate and exact solutions, as shown in the presented tables and figures.

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Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions

Ahmed

2024

J Nonlinear Math Phys

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Parameter Uniform Numerical Method for a Weakly Coupled System of Second Order Singularly Perturbed Turning Point Problem with Robin Boundary Conditions

Cited by 1 publication

References 16 publications

Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions

Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions

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