Uniformly convergent numerical method for singularly perturbed parabolic differential equations with non-smooth data and large negative shift

Singularly perturbed parabolic differential problems with non-smooth data and a large negative shift in the space variable were studied. The proposed scheme is based on method of lines, nonstandard finite difference for discretization, followed by backward Euler resulting system initial value time discretization. stability uniform convergence are investigated proved. As demonstrated theoretically experimentally, uniformly convergent an order two spatial direction one temporal direction. maximum absolute errors rate various perturbation parameters mesh size values tabulated model examples.