A numerical scheme for singularly perturbed delay differential equations of convection-diffusion type on an adaptive grid. (English) Zbl 1488.65158
Summary: In this paper, an adaptive mesh strategy is presented for solving singularly perturbed delay differential equation of convection-diffusion type using second order central finite difference scheme. Layer adaptive meshes are generated via an entropy production operator. The details of the location and width of the layer is not required in the proposed method unlike the popular layer adaptive meshes mainly by Bakhvalov and Shishkin. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
MSC:
| 65L03 | Numerical methods for functional-differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
Keywords:
singular perturbation; entropy like variable; delay differential equation; layer adaptive meshes; central finite difference scheme; convection-diffusion problemReferences:
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