Affiliation:
1. School of Statistics and Mathematics Shandong University of Finance and Economics Jinan PR China
2. School of Mathematics Shandong University Jinan PR China
Abstract
AbstractIn this paper, a novel numerical scheme is proposed to numerically solve the fractional activator–inhibitor system, which is a coupled two‐dimensional nonlinear model. In the temporal direction, we employ the Grünwald–Letnikov formula, in spatial direction, the Legendre spectral method is used. In terms of the error splitting argument technique, an optimal error estimate of the numerical scheme is obtained without any time‐step size conditions, while the usual analysis for high‐dimensional nonlinear fractional problems always required certain time‐step restrictions dependent on the spatial mesh size. Some numerical results are given to justify the theoretical analysis.
Funder
China Postdoctoral Science Foundation
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Subject
Applied Mathematics,Computational Mechanics