Nonstandard finite difference method for solving singularly perturbed time-fractional delay parabolic reaction-diffusion problems

This work addresses the singularly perturbed time-fractional delay parabolic reaction-diffusion of initial boundary value problems. The temporal derivative’s discretization is handled by the Caputo fractional derivative combined with the implicit Euler technique with uniform step size. It also utilizes the nonstandard finite difference approach for the spatial derivative. The scheme has been demonstrated to converge and has an accuracy of  O(h^{2}+(\Delta t^{2-\alpha})). To assess the suitability of the approach, two model examples are taken into consideration. The findings, which are provided in tables and figures, illustrate that the system has twin layers at the end of space domain and is uniformly convergent.

Nonstandard finite difference method for solving singularly perturbed time-fractional delay parabolic reaction-diffusion problems Keywords:

Nonstandard finite difference , time-fractional , delay parabolic reaction-diffusion , convergence Analysis