New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation

Abstract

In this paper, new group iterative schemes are developed for the numerical solution of two-dimensional anomalous fractional sub-diffusion equation subject to specific initial and Dirichlet boundary conditions. The new group relaxation iterative schemes are derived from the combination of standard and rotated (skewed) five-point modified implicit finite difference approximations. The results derived from the conducted numerical experiments show that fractional explicit de-coupled group (FEDG) iterative method has a significantly less computational cost in terms of CPU-timings as compared to the other iterative schemes, without threatening compromising accuracies.

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

“…Fractional calculus (FC) and fuzzy concepts are vital instruments that deal with ambiguity, recognise emotional or ambiguous conditions, and provide more general mathematical solutions [1][2][3][4][5][6][7][8]. Fuzzy sets are also an excellent approach to imitate the uncertainty that results from being ambiguous and unclear.…”