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Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy. (English) Zbl 1120.65089

Some numerical methods are studied for one-dimensional singularly perturbed differential-difference equations M. Stynes and H.-G. Roos [Appl. Numer. Math. 23, No. 3, 361–374 (1997; Zbl 0877.65055)] proposed a midpoint scheme and a hybrid scheme for singularly perturbed two-point boundary-value problems on a piecewise-uniform Shishkin mesh.

In this paper, the above said schemes are applied to the singularly perturbed differential-difference equations on the Shishkin mesh. Error estimates are obtained, and some numerical examples are carried out.

MSC:
65L10Boundary value problems for ODE (numerical methods)
34K28Numerical approximation of solutions of functional-differential equations
34K10Boundary value problems for functional-differential equations
65L70Error bounds (numerical methods for ODE)
65L50Mesh generation and refinement (ODE)