Charles. Simpson, Arthur
(2001)
Numerical methods for the solution of fractional differential equations.
PhD thesis, University of Liverpool.
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Abstract
The fractional calculus is a generalisation of the calculus of Newton and Leibniz. The substitution of fractional differential operators in ordinary differential equations substantially increases their modelling power. Fractional differential operators set exciting new challenges to the computational mathematician because the computational cost of approximating fractional differential operators is of a much higher order than that necessary for approximating the operators of classical calculus. 1. We present a new formulation of the fractional integral. 2. We use this to develop a new method for reducing the computational cost of approximating the solution of a fractional differential equation. 3. This method can be implemented with two levels of sophistication. We compare their rates of convergence, their algorithmic complexity, and their weight set sizes so that an optimal choice, for a particular application, can be made. 4. We show how linear multiterm fractional differential equations can be approximated as systems of fractional differential equations of order at most 1.
| Item Type: | Thesis (PhD) |
|---|---|
| Depositing User: | Symplectic Admin |
| Date Deposited: | 23 Oct 2023 10:59 |
| Last Modified: | 23 Oct 2023 11:15 |
| DOI: | 10.17638/03176149 |
| Copyright Statement: | Copyright © and Moral Rights for this thesis and any accompanying data (where applicable) are retained by the author and/or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3176149 |
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