Numerical investigation of singularly perturbed time lag parabolic differential-difference equations

This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the <i>θ</i> method ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn></mml:math> ) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme. The applicability of the proposed approach is confirmed through some numerical examples. Furthermore, we have improved the convergence from almost first to almost second order.