Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Mesfin Mekuria Woldaregay1, Gemechis File Duressa2
1Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. msfnmkr02@gmail.com.
Objectives:
Numerical 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 [Formula: see text]-method in time discretization and non-standard finite difference method in space discretization.
Result:
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. Numerical examples are considered to validate the theoretical findings.
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