Higher order numerical methods for solving fractional differential equations
Abstract
In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is O(h^(3−α)). Our second approach is based on discretisation of the integral form of the fractional differential equation and we obtain a fractional Adams-type method for a nonlinear fractional differential equation of any order α >0. The order of convergence of the numerical method is O(h^3) for α ≥ 1 and O(h^(1+2α)) for 0 < α ≤ 1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results.Citation
Yan, Y., Pal, K., & Ford, N. J. (2014). Higher order numerical methods for solving fractional differential equations. BIT Numerical Mathematics, 54(2), 555-584. doi:10.1007/s10543-013-0443-3Publisher
SpringerJournal
BIT Numerical MathematicsAdditional Links
http://link.springer.com/10.1007/s10543-013-0443-3Type
ArticleLanguage
enDescription
The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-013-0443-3ISSN
1572-9125ae974a485f413a2113503eed53cd6c53
10.1007/s10543-013-0443-3
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