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A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations
Authors:Gabil M Amiraliyev  Fevzi Erdogan
Institution:(1) Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, China;(2) Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
Abstract:This study deals with the singularly perturbed initial value problem for a quasilinear first-order delay differential equation. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the method is first order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.
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