@Article{NMTMA-14-1,
author = {Zhenning, Cai and Junying, Cao and Zhenning, Cai},
title = {Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {1},
pages = {71--112},
abstract = {<p style="text-align: justify;">We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing
the domain into a number of subintervals, and applying the quadratic interpolation
on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order 3 − $ν$ can be rigorously
proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear
case. Some numerical examples are given to validate our theoretical results.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2020-0039},
url = {https://global-sci.com/article/90292/numerical-analysis-of-a-high-order-scheme-for-nonlinear-fractional-differential-equations-with-uniform-accuracy}
}