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High order algorithms for numerical solution of fractional differential equations
Asl, Mohammad S. Javidi, Mohammad Yan, Yubin
Asl, Mohammad S.
Javidi, Mohammad
Yan, Yubin
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2021-02-17
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Abstract
In this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then
the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.
Citation
Asl, M. S., Javidi, M. & Yan, Y. (2021). High order algorithms for numerical solution of fractional differential equations. Advances in Difference Equations, 111. https://doi.org/10.1186/s13662-021-03273-4
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SpringerOpen
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Advances in Difference Equations
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This document is the Accepted Manuscript version of a published work that appeared in final form in [Advances in Difference Equations]. To access the final edited and published work see http://dx.doi.org/10.1186/s13662-021-03273-4.
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ISSN
1687-1839
EISSN
1687-1847