Fitted finite difference method for singularly perturbed delay differential equations

Abstract

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.

Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

“…[9]): u " ( t ) = -U ' ( t ) -U ( t -1) + 1, 0 < t < 2, U{t) = 1, (7'(0) = -1 , -1 < t < 0, (4.4) where the solution is given by m = e_ t, 0 < t < 1,…”

A numerical scheme for a weakly coupled system of singularly perturbed delay differential equations on an adaptive mesh

“…Singularly perturbed delay differential equations arise in the mathematical modelling of biological sciences, applied mathematics, and several branches of engineering such as the modeling of biological oscillators, 9 immune response, 10 dynamics of networks of two identical amplifiers, 11 mathematical ecology, 12 population dynamics, 13 etc. The numerical treatment of singularly perturbed delay differential equations with large delays can be found in Lange and Miura, 14 Amiraliyev and Erdogan, 15 Amiraliyev and Cimen, 16 Amiraliyeva et al, 17 Erdogan and Amiraliyev, 18 Subburayan and Ramanujam, 19 Chakravarthy et al, 20 Bansal and Sharma 21 . Very little literature is available for numerical treatment of system of singularly perturbed delay differential equations.…”

A higher order finite element method with modified graded mesh for singularly perturbed two‐parameter problems

“…This choice of monitor function leads to an optimal second-order parameter uniform convergence. In Cen et al 18 and Erdogan and Amiraliyev, 19 the authors deal with initial value problems involving two parameters. In Cen et al, 20 assumptions posed on the coefficients suggests that the differential operator does not satisfy the maximum principle.…”