@Article{NMTMA-14-3,
author = {Shimin, Guo and Yan, Wenjing and Mei, Liquan and Ying, Wang and Wang, Lingling},
title = {A Linearized Spectral-Galerkin Method for Three-Dimensional Riesz-Like Space Fractional Nonlinear Coupled Reaction-Diffusion Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {3},
pages = {738--772},
abstract = {<p style="text-align: justify;">In this paper, we establish a novel fractional model arising in the chemical reaction and develop an efficient spectral method for the three-dimensional
Riesz-like space fractional nonlinear coupled reaction-diffusion equations. Based on
the backward difference method for time stepping and the Legendre-Galerkin spectral method for space discretization, we construct a fully discrete numerical scheme
which leads to a linear algebraic system. Then a direct method based on the matrix
diagonalization approach is proposed to solve the linear algebraic system, where the
cost of the algorithm is of a small multiple of $N^4$ ($N$ is the polynomial degree in
each spatial coordinate) flops for each time level. In addition, the stability and convergence analysis are rigorously established. We obtain the optimal error estimate
in space, and the results also show that the fully discrete scheme is unconditionally
stable and convergent of order one in time. Furthermore, numerical experiments
are presented to confirm the theoretical claims. As the applications of the proposed
method, the fractional Gray-Scott model is solved to capture the pattern formation
with an analysis of the properties of the fractional powers.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2020-0093},
url = {https://global-sci.com/article/90318/a-linearized-spectral-galerkin-method-for-three-dimensional-riesz-like-space-fractional-nonlinear-coupled-reaction-diffusion-equations}
}