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

doi:10.1007/s42967-019-00043-8

Communications on Applied Mathematics and Computation ›› 2020, Vol. 2 ›› Issue (2): 179-199.doi: 10.1007/s42967-019-00043-8

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

Junying Cao¹, Ziqiang Wang¹, Chuanju Xu²

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

收稿日期:2019-01-30 修回日期:2019-08-04 出版日期:2020-06-20 发布日期:2020-02-19
通讯作者: Chuanju Xu E-mail:cjxu@xmu.edu.cn
基金资助:
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).

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

Junying Cao¹, Ziqiang Wang¹, Chuanju Xu²

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:2019-01-30 Revised:2019-08-04 Online:2020-06-20 Published:2020-02-19
Contact: Chuanju Xu E-mail:cjxu@xmu.edu.cn
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).

摘要/Abstract

摘要： 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.

关键词: Caputo-Fabrizio derivative, Fractional diferential equations, High-order numerical scheme

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

中图分类号:

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.

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

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

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