A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations |
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Authors: | Gabil M Amiraliyev Fevzi Erdogan |
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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 |
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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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Keywords: | |
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