Abstract
This article introduces the fractional variable order (VO) Gray-Scott model using the notion of VO fractional derivative in the Caputo sense. An efficient numerical method has been designed based on the VietaâLucas polynomial and the spectral collocation method for solving this model. The designed technique converts the concerned model into a nonlinear algebraic system of equations, which can be solved by Newtonâs iterative method. In this article, we have illustrated the convergence analysis of the approximation and shown that a high order of convergence can be achieved despite a smaller number of approximations. A few numerical results are presented in order to verify the reliability and accuracy of the demonstrated scheme. The results of absolute errors for the considered Gray-Scott model with its exact solution show that the technique is very suitable for finding the solutions to the said kind of complex physical problem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have