Abstract
In this article, we study the numerical solution of singularly perturbed system of boundary-value problems for second-order ordinary differential equations of reaction–diffusion type. The solution of these problems exhibits twin boundary layers at both the ends of the domain. To obtain the numerical solution of these problems, we apply the nonsymmetric discontinuous Galerkin FEM with interior penalties (NIPG method). Also, we proved that the method is \(O(N^{-1}\ln N)^{k}\) accurate in energy norm, on Shishkin mesh with N number of intervals and k degree of piecewise polynomial. Numerical results are presented to support the theoretical results.
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Singh, G., Natesan, S. (2018). A Uniformly Convergent NIPG Method for a Singularly Perturbed System of Reaction–Diffusion Boundary-Value Problems. In: Ghosh, D., Giri, D., Mohapatra, R., Sakurai, K., Savas, E., Som, T. (eds) Mathematics and Computing. ICMC 2018. Springer Proceedings in Mathematics & Statistics, vol 253. Springer, Singapore. https://doi.org/10.1007/978-981-13-2095-8_33
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DOI: https://doi.org/10.1007/978-981-13-2095-8_33
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