Abstract
Fractional differential equation approach is frequently used to describe long-term interactions in nonlinear systems. However, it results in difficulty in inverse problems as well as the numerical treatment. Numerical analysis of intermediate value problems and the well-posedness are investigated in this study. Two high order numerical methods for solving intermediate value problems are proposed. Convergence and sensitivity analysis are provided. A comparison is provided by a well-chosen example. The estimated order of the convergence shows the sharpness of our analysis.
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Acknowledgements
This study was financially supported by National Natural Science Foundation of China (Grant no. 62076141) and Sichuan Province Youth Science and Technology Innovation Team (Grant no. 2019JDTD0015).
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Communicated by Agnieszka Malinowska.
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Yang, G., Shiri, B., Kong, H. et al. Intermediate value problems for fractional differential equations. Comp. Appl. Math. 40, 195 (2021). https://doi.org/10.1007/s40314-021-01590-8
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DOI: https://doi.org/10.1007/s40314-021-01590-8
Keywords
- Terminal value problem
- Fractional differential equations
- Discrete collocation methods
- Well-posedness
- Piecewise polynomials spaces