Uniformly Convergent Difference Scheme for a Semilinear Reaction-Diffusion Problem on Shishikin mesh
arXiv:1712.013135 citationsh-index: 3
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Provides a theoretical convergence guarantee for numerical methods on a specific class of boundary value problems, but the contribution is incremental as it extends known techniques to a semilinear case.
The paper develops two difference schemes for a singularly perturbed semilinear reaction-diffusion problem on a Shishkin mesh, proving ε-uniform convergence and confirming it with four numerical experiments.
In this paper we consider two difference schemes for numerical solving of a one--dimensional singularly perturbed boundary value problem. We proved an $\varepsilon$--uniform convergence for both difference schemes on a Shiskin mesh. Finally, we present four numerical experiments to confirm the theoretical results.