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A fractional Adams–Simpson-type method for nonlinear fractional ordinary differential equations with non-smooth data.
- Source :
-
BIT: Numerical Mathematics . Mar2023, Vol. 63 Issue 1, p1-21. 21p. - Publication Year :
- 2023
-
Abstract
- We propose a fractional Adams–Simpson-type method for nonlinear fractional ordinary differential equations with fractional order α ∈ (0 , 1) . In our method, a nonuniform mesh is used so that the optimal convergence order can be recovered for non-smooth data. By developing a modified fractional Grönwall inequality, we prove that the method is unconditionally convergent under the local Lipschitz condition of the nonlinear term, and show that with a proper mesh parameter, the method can achieve the optimal convergence order 3 + α even if the given data is not smooth. Under very mild conditions, the nonlinear stability of the method is analyzed by using a perturbation technique. The extensions of the method to multi-term nonlinear fractional ordinary differential equations and multi-order nonlinear fractional ordinary differential systems are also discussed. Numerical results confirm the theoretical analysis results and demonstrate the effectiveness of the method for non-smooth data. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00063835
- Volume :
- 63
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- BIT: Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 161614331
- Full Text :
- https://doi.org/10.1007/s10543-023-00952-4