@Article{AAMM-9-3,
author = {Zhou, Xiaojun and Xu, Chuanju},
title = {Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {3},
pages = {574--595},
abstract = {<p style="text-align: justify;">In this paper, we consider the numerical method that is proposed and analyzed in [J. Cao and C. Xu, J. Comput. Phys., 238 (2013), pp. 154–168] for the fractional
ordinary differential equations. It is based on the so-called block-by-block approach,
which is a common method for the integral equations. We extend the technique to
solve the nonlinear system of fractional ordinary differential equations (FODEs) and
present a general technique to construct high order schemes for the numerical solution
of the nonlinear coupled system of fractional ordinary differential equations (FODEs).
By using the present method, we are able to construct a high order schema for nonlinear system of FODEs of the order $α$, $α&gt;0$. The stability and convergence of the schema
is rigorously established. Under the smoothness assumption $f,g ∈ C^4[0,T]$, we prove
that the numerical solution converges to the exact solution with order $3+α$ for $0&lt;α≤1$ and order $4$ for $α&gt;1$. Some numerical examples are provided to confirm the theoretical
claims.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1054},
url = {https://global-sci.com/article/73266/numerical-solution-of-the-coupled-system-of-nonlinear-fractional-ordinary-differential-equations}
}