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The numerical solution of fractional and distributed order differential equations
Connolly, Joseph A.
Connolly, Joseph A.
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2004-12
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Abstract
Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that it extends the concept of a derivative (integral) to include non-integer orders. Effective mathematical modelling using Fractional Differential Equations (FDEs) requires the development of reliable flexible numerical methods.
The thesis begins by reviewing a selection of numerical methods for the solution of Single-term and Multi-term FDEs.
We then present:
1. a graphical technique for comparing the efficiency of numerical methods. We use this to compare Single-term and Multi-term methods and give recommendations for which method is best for any given FDE.
2. a new method for the solution of a non-linear Multi-term Fractional Dif¬ferential Equation.
3. a sequence of methods for the numerical solution of a Distributed Order Differential Equation.
4. a discussion of the problems associated with producing a computer program for obtaining the optimum numerical method for any given FDE.
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University of Liverpool
University College Chester
University College Chester
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Thesis or dissertation
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en
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