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Abstract
ObjectivesNumerical treatment of singularly perturbed parabolic delay differential equation is considered. Solution of the equation exhibits a boundary layer, which makes it difficult for numerical computation. Accurate numerical scheme is proposed using theta-method in time discretization and non-standard finite difference method in space discretization.ResultStability and uniform convergence of the proposed scheme is investigated. The scheme is uniformly convergent with linear order of convergence before Richardson extrapolation and second order convergent after Richardson extrapolation. Numerical examples are considered to validate the theoretical findings.
Highlights
Singularly perturbed delay differential equation (SPDDE) is a differential equation in which its highest order derivative term is multiplied by small perturbation parameter and involving at least one delay term
A number of papers have been published on numerical treatment of time dependent singularly perturbed differential difference equations
The developed scheme is based on non standard Finite difference method (FDM)
Summary
Stability and uniform convergence of the proposed scheme is investigated. The scheme is uniformly convergent with linear order of convergence before Richardson extrapolation and second order convergent after Richardson extrapolation.
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