LIMIT POINT, STRONG LIMIT POINT AND DIRICHLET CONDITIONS FOR DISCRETE HAMILTONIAN SYSTEMS

Zhaowen Zheng; Jing Shao

doi:10.11948/20190042

2020 Volume 10 Issue 3

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Zhaowen Zheng, Jing Shao. LIMIT POINT, STRONG LIMIT POINT AND DIRICHLET CONDITIONS FOR DISCRETE HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 875-891. doi: 10.11948/20190042

Citation:

Zhaowen Zheng, Jing Shao. LIMIT POINT, STRONG LIMIT POINT AND DIRICHLET CONDITIONS FOR DISCRETE HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 875-891. doi: 10.11948/20190042

LIMIT POINT, STRONG LIMIT POINT AND DIRICHLET CONDITIONS FOR DISCRETE HAMILTONIAN SYSTEMS

Zhaowen Zheng^1, ,,
Jing Shao²

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
2.
Department of Mathematics, Jining University, Qufu 273155, China

Corresponding author: Email address:zhwzheng@126.com (Z. Zheng)
Fund Project: The authors were supported by National Natural Science Foundation of China (11671227), National Science Foundation of Shandong (ZR2019MA034, ZR2018LA004) and Science and Technology Project of High Schools of Shandong (J18KA220, J18KB107)

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: 39A70, 34B20, 47B25

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References

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