Diffusive Representations of Fractional Differential Operators and Their Use in Numerical Fractional Calculus

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• Kai Diethelm (University of Applied Sciences Würzburg-Schweinfurt)
• Monday 07 March 2022, 14:00-15:00
• Seminar Room 2, Newton Institute.

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FDE2 - Fractional differential equations

The infinite state representation, also known as the diffusive representation, is a way to express a fractional differential operator in the form of an integral, typically over the positive half-line, whose integrand can be written as the solution to a relatively simple initial value problem for a first order differential equation. As such, it permits to approximately compute fractional derivatives by the application of a numerical integration method to an integrand obtained by numerically solving the first order initial value problem. Compared to traditional methods, applying this approach as the underlying discretization of the fractional derivative in a solver for fractional differential equations has significant advantages with respect to run time and memory requirements of the algorithm. However, the algorithms obtained in this way depend on a number of parameters that are not trivial to interpret and whose influence on the accuracy of the final result is often unclear. In this talk, we will present an investigation of these dependencies and present some guidelines on how to choose the parameters.

This talk is part of the Isaac Newton Institute Seminar Series series.

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