Exponentially fitted robust scheme for the solution of singularly perturbed delay parabolic differential equations with integral boundary condition

Abstract In this paper, an exponentially fitted finite difference method is developed to solve singularly perturbed delay parabolic partial differential equations having a large delay on the spatial variable with an integral boundary condition on the right side of the domain. The problem's solution exhibits an interior layer and a parabolic boundary layer on both ends of the spatial domain. Simpson's rule is applied to treat the integral boundary condition. Uniform convergence analysis has been carried out, and it is observed that the method is first-order convergent in the time direction and second-order in the spatial direction. Numerical examples and results are considered to validate the scheme's applicability, and it also improves the results of the methods existing in the literature. MSC Classification: 65L11 , 65M06 , 65M12.