Communications on Applied Mathematics and Computation >

2020 , Vol. 2 >Issue 2: 179 - 199

DOI: https://doi.org/10.1007/s42967-019-00043-8

A High-Order Scheme for Fractional Ordinary Diferential Equations with the Caputo-Fabrizio Derivative

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  • 1 School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China;
    2 School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientifc Computing, Xiamen University, Xiamen 361005, China

Received date: 2019-01-30

  Revised date: 2019-08-04

  Online published: 2020-02-19

Supported by

This research was supported by the National Natural Science Foundation of China (Grant numbers 11501140, 51661135011, 11421110001, and 91630204) and the Foundation of Guizhou Science and Technology Department (No. [2017]1086). The frst author would like to acknowledge the fnancial support by the China Scholarship Council (201708525037).

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Abstract

In this paper, we consider numerical solutions of fractional ordinary diferential equations with the Caputo-Fabrizio derivative, and construct and analyze a high-order time-stepping scheme for this equation. The proposed method makes use of quadratic interpolation function in sub-intervals, which allows to produce fourth-order convergence. A rigorous stability and convergence analysis of the proposed scheme is given. A series of numerical examples are presented to validate the theoretical claims. Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique. The advantage of our scheme is that the solution can be obtained step by step, which is cheaper than a block-by-block-based approach.

Key words： Caputo-Fabrizio derivative; Fractional diferential equations; High-order numerical scheme

Cite this article

Junying Cao, Ziqiang Wang, Chuanju Xu . A High-Order Scheme for Fractional Ordinary Diferential Equations with the Caputo-Fabrizio Derivative[J]. Communications on Applied Mathematics and Computation, 2020 , 2(2) : 179 -199 . DOI: 10.1007/s42967-019-00043-8

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