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BIT Numerical Mathematics

Erschienen in:

12.05.2020

Numerical method with fractional splines for a subdiffusion problem

verfasst von: Carla Jesus, Ercília Sousa

Erschienen in: BIT Numerical Mathematics | Ausgabe 4/2020

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Abstract

We consider a subdiffusion problem described by a time fractional Riemann–Liouville derivative of order \(0<\alpha <1\). The main purpose of this work is to show how we can apply fractional splines of order \(0<\beta \le 1\) to approximate a fractional integral and hence how to solve the subdiffusion problem using this approach. To discuss the convergence of the numerical method we present the error bounds for the fractional splines and the fractional integral approximations and study the von Neumann stability analysis. We observe that, depending on the smoothness of the solution, the order of convergence will be affected by the values of \(\alpha \) and \(\beta \). Numerical tests are presented along the work to highlight several properties of the fractional splines and the numerical tests in the end illustrate the performance of the numerical method.

Vorheriger Artikel Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Nächster Artikel Approximation of the matrix exponential for matrices with a skinny field of values

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Titel: Numerical method with fractional splines for a subdiffusion problem
verfasst von: Carla Jesus
Ercília Sousa
Publikationsdatum: 12.05.2020
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 4/2020
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-020-00808-1

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