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A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations

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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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Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics, Yuzuncu yil University, 65080, Van, Turkey

    Gabil M. Amiraliyev & Fevzi Erdogan

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  1. Gabil M. Amiraliyev
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  2. Fevzi Erdogan
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Correspondence to Gabil M. Amiraliyev.

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Amiraliyev, G.M., Erdogan, F. A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations. Numer Algor 52, 663–675 (2009). https://doi.org/10.1007/s11075-009-9306-z

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  • DOI: https://doi.org/10.1007/s11075-009-9306-z

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