A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay

Awoke Andargie Tiruneh, Getachew Adamu Derese, Dagnachew Mengstie Tefera, Palle Kiran
2022 International Journal of Mathematics and Mathematical Sciences  
In this paper, we design and investigate a higher order ε -uniformly convergent method to solve singularly perturbed parabolic reaction-diffusion problems with a large time delay. We use the Crank–Nicolson method for the time derivative, while the spatial derivative is discretized using a nonstandard finite difference approach on a uniform mesh. Furthermore, to improve the order of convergence, we used the Richardson extrapolation technique. The designed scheme converges independent of the
more » ... rbation parameter ( ε -uniformly convergent) and also achieves fourth-order convergent in both time and spatial variables. Two model examples are considered to demonstrate the applicability of the suggested method. The proposed method produces better accuracy and a higher rate of convergence than some methods that appear in the literature.
doi:10.1155/2022/5625049 fatcat:guxnenqikfd35ejd5c7ounqmy4