Article
A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations
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Abstract
The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.
Keywords
Delay differential equation, Singular perturbation, Finite difference scheme, Piecewise-uniform mesh, Error estimates, 34D15, 65L10, 65L11, 65L12
Citation
Erdogan, F., Sakar, M. G., & Saldır, O. (2020). A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences, 5(1), 425–436. https://doi.org/10.2478/amns.2020.1.00040
F. Erdogan, M. G. Sakar and O. Saldır, “A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 1, pp. 425–436, 2020, doi: 10.2478/amns.2020.1.00040.
Erdogan F, Sakar MG, Saldır O. A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences. 2020;5(1):425–436. doi:10.2478/amns.2020.1.00040.
Erdogan, F., Sakar, M. G. and Saldır, O. (2020), ‘A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations’, Applied Mathematics and Nonlinear Sciences, 5(1), pp. 425–436. Available at: https://doi.org/10.2478/amns.2020.1.00040.
Erdogan, Fevzi, et al. “A Finite Difference Method on Layer-adapted Mesh for Singularly Perturbed Delay Differential Equations.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 1, 2020, pp. 425–436. https://doi.org/10.2478/amns.2020.1.00040.
Erdogan, Fevzi, Mehmet Giyas Sakar, and Onur Saldır. “A Finite Difference Method on Layer-adapted Mesh for Singularly Perturbed Delay Differential Equations.” Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 425–436. https://doi.org/10.2478/amns.2020.1.00040.
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Published by: Engineering Journals
