Abstract
In this work we study a system of M( ≥ 2) first-order singularly perturbed ordinary differential equations with given initial conditions. The leading term of each equation is multiplied by a distinct small positive parameter, which induces overlap** layers. A maximum principle does not, in general, hold for this system. It is discretized using backward Euler difference scheme for which a general convergence result is derived that allows to establish nodal convergence of O(N − 1ln N) on the Shishkin mesh and O(N − 1) on the Bakhvalov mesh, where N is the number of mesh intervals and the convergence is robust in all of the parameters. Numerical experiments are performed to support the theoretical results.
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Kumar, S., Kumar, M. Parameter-robust numerical method for a system of singularly perturbed initial value problems. Numer Algor 59, 185–195 (2012). https://doi.org/10.1007/s11075-011-9483-4
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DOI: https://doi.org/10.1007/s11075-011-9483-4