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.