A New Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems

Abstract

This study is related to a novel numerical technique for solving the singularly perturbed reaction-diffusion boundary value problems. First, explicit boundaries for the solution of the problem are established. Then, a finite difference scheme is established on a uniform mesh supported by the method of integral identities using the remainder term in integral form and the exponential rules with weight. The uniform convergence and stability of these schemes are investigated concerning the perturbation parameter in the discrete maximum norm. At last, the numerical results that provide theoretical results are presented.

Keywords

• Singular perturbation
• Reaction-Diffusion
• Uniform mesh
• Boundary layer
• Numerical solution

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