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Convergence and stability of block boundary value methods applied to nonlinear fractional differential equations with Caputo derivatives.
- Source :
-
Applied Numerical Mathematics . Jan2019, Vol. 135, p367-380. 14p. - Publication Year :
- 2019
-
Abstract
- Abstract In this paper, by combining the p -order block boundary value methods with the m -th Lagrange interpolation, a class of new numerical methods for solving nonlinear fractional differential equations with the γ -order (0 < γ < 1) Caputo derivatives are obtained. It is proved under some appropriate conditions that the induced methods are convergent of order min { p , m − γ + 1 } and globally stable. Several numerical examples are given to illustrate the theoretical results and the computational effectiveness and accuracy of the methods. Highlights • This paper deals with numerical computation and analysis for nonlinear fractional differential equations (FDEs) with γ -order Caputo derivatives. • A class of extended block boundary value methods (EBBVMs) for solving the FDEs are obtained. • The EBBVMs are proved to be convergent of order min { p , m − γ + 1 } and globally stable under the appropriate conditions. • Several numerical examples are given to illustrate the theoretical results and the computational effectiveness and accuracy of the methods. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 135
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 132106003
- Full Text :
- https://doi.org/10.1016/j.apnum.2018.09.010