Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy
Year: 2021
Author: Zhenning Cai, Junying Cao, Zhenning Cai
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 71–112
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0039
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 71–112
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 42
Keywords: Caputo derivative fractional ordinary differential equations high-order numerical scheme stability and convergence analysis.