New approach of convergent numerical method for singularly perturbed delay parabolic convection-diffusion problems

In this paper, a parameter-uniform convergent numerical scheme is provided for solving singularly perturbed parabolic convection-diffusion differential equations with large delay. A priori bounds on the exact solution and its derivatives derived by asymptotic analysis of problem are provided.. The discretized Crank-Nicolson method uniform mesh in time direction fitted operator upwind finite difference spatial direction. fitting factor from zeroth-order expansion then introduced term containing singular perturbation parameter. convergence given proposed using barrier function approach Peano kernel. We proved uniformly first -order space second order time, both independent Numerical experiments presented to support theoretical findings.