Parameter-uniform numerical treatment of singularly perturbed parabolic delay differential equations with nonlocal boundary conditions

This paper focuses on solving singularly perturbed parabolic equations of the convection-diffusion type with a large negative spatial shift and an integral boundary condition. A higher-order uniformly convergent numer-ical approach is proposed that uses Crank–Nicolson and a hybrid finite difference approximation on a piece-wise uniform Shishkin mesh. Simp-son’s 1/3 integration rule is used to treat the integral boundary condition. The proposed method has been shown to achieve almost second-order uni-form convergence. The computational results derived from the numerical experiment are consistent with the theoretical estimates. Furthermore, the method produces a more accurate result than certain other methods in the literature.