An adaptive moving grid method for a system of singularly perturbed initial value problems

• Autores: Li-Bin Liu, Yanping Chen
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 274, Nº 1, 2015, págs. 11-22
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.06.022
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• Resumen

  • A system of first-order singularly perturbed initial value problems is considered. The system is discretized by a backward Euler difference scheme for which a priori error analysis in the maximum norm is constructed. It is shown from the a priori error bound that there exists a mesh with N subintervals that gives optimal error bound of O(N-1) which is robust with respect to the perturbation parameters. A partly heuristic argument based on a priori error analysis leads to a suitable monitor function. Based on an a posteriori error bound, a first-order rate of convergence, independent of all perturbation parameters, is established. A linear and a nonlinear examples are tested, and the numerical results are provided to demonstrate the effectiveness of our adaptive moving grid method.