A BLOCK-BY-BLOCK METHOD FOR THE IMPULSIVE FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS

Junying Cao; Lizhen Chen; Ziqiang Wang

doi:10.11948/20180312

2020 Volume 10 Issue 3

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Junying Cao, Lizhen Chen, Ziqiang Wang. A BLOCK-BY-BLOCK METHOD FOR THE IMPULSIVE FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 853-874. doi: 10.11948/20180312

Citation:

Junying Cao, Lizhen Chen, Ziqiang Wang. A BLOCK-BY-BLOCK METHOD FOR THE IMPULSIVE FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 853-874. doi: 10.11948/20180312

A BLOCK-BY-BLOCK METHOD FOR THE IMPULSIVE FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS

1.
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
2.
Beijing Computational Science Research Center, Beijing 100193, China
3.
Department of Mathematics, National University of Singapore, Singapore 119076, Singapore

Corresponding author: Email address:wangzq@lsec.cc.ac.cn(Z. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China (Grant numbers 11901135, 11961009, 11671166, U1530401), Foundation of Guizhou Science and Technology Department ([2017]1086, [2020]1Y015), The first author would like to acknowledge the financial support by the China Scholarship Council (201708525037)

Abstract

Abstract

In this paper, a block-by-block numerical method is constructed for the impulsive fractional ordinary differential equations (IFODEs). Firstly, the stability and convergence analysis of the scheme are established. Secondly, the numerical solution which converges to the exact solution with order $ 3+\gamma $ for $ 0<\gamma<1 $ is proved, where $ \gamma $ is the order of the fractional derivative. Finally, a series of numerical examples are carried out to verify the correctness of the theoretical analysis.
- Impulsive fractional ordinary differential equations /
- block-by-block method /
- stability analysis /
- convergence analysis
MSC: 65L12

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References

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