Open AccessA spectral collocation method for the coupled system of nonlinear fractional differential equations
Author(s) -
Xiaojun Zhou,
AUTHOR_ID,
Yue Dai
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022314
Subject(s) - legendre polynomials , mathematics , nonlinear system , collocation method , discretization , fractional calculus , collocation (remote sensing) , spectral method , mathematical analysis , differential equation , ordinary differential equation , physics , computer science , quantum mechanics , machine learning
This paper analyzes the coupled system of nonlinear fractional differential equations involving the caputo fractional derivatives of order $ \alpha\in(1, 2) $ on the interval (0, T). Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations, then the resulting equation is discretized by using a spectral method based on the Legendre polynomials. We have constructed a Legendre spectral collocation method for the coupled system of nonlinear fractional differential equations. The error bounds under the $ L^2- $ and $ L^{\infty}- $norms is also provided, then the theoretical result is validated by a number of numerical tests.