Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition

Abstract This paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter multiplied higher order derivative, which gives layers, due to term, one more layer occurs rectangle numerical method comprising standard finite difference scheme piecewise uniform mesh (Shishkin mesh) of $N_{r} \times N_{t}$ N r × t elements condensing layers suggested, it proved be parameter-uniform. Also, convergence almost two space variable time variable. Numerical examples are proposed validate theory.