Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method

A new finite difference collocation algorithm has been introduced with the help of Fibonacci polynomial and then applied to one super and two sub-diffusion problems having an exact solution. It has also been shown that numerical error obtained with the investigated method is more accurate than previously existing methods. Fractional order reaction advection sub-diffusion equation containing Caputo and Riemann-Liouville fractional derivatives has been solved and the effects due to change in various parameters presented in the considered model with the graphical representation have been discussed. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

A new finite difference collocation algorithm utilizing Fibonacci polynomial was introduced and applied to a super diffusion problem and two sub-diffusion problems with exact solutions. It was demonstrated that the numerical error obtained from this method is more accurate than previously existing methods. The study also solved a fractional order reaction advection sub-diffusion equation and discussed the effects of parameter changes in the model with graphical representation.