Numerical Approximation of a Class of Time-Fractional Differential Equations

Aleksandra Delić (), Boško S. Jovanović () and Sandra Živanović ()
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Aleksandra Delić: University of Belgrade
Boško S. Jovanović: University of Belgrade
Sandra Živanović: University of Belgrade

A chapter in Computational Mathematics and Variational Analysis, 2020, pp 55-79 from Springer

Abstract: Abstract We consider a class of linear fractional partial differential equations containing two time-fractional derivatives of orders α, β ∈ (0, 2) and elliptic operator on space variable. Three main types of such equations with α and β in the corresponding subintervals were determined. The existence of weak solutions of the corresponding initial-boundary value problems has been proved. Some finite difference schemes approximating these problems are proposed and their stability is proved. Estimates of their convergence rates, in special discrete energetic Sobolev’s norms, are obtained. The theoretical results are confirmed by numerical examples.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-44625-3_4

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DOI: 10.1007/978-3-030-44625-3_4

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