High Order Difference Schemes for Fractional Parabolic Equations - Bayramoglu Erguner, Serife Rabia
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This book is devoted to the numerical solution of the fractional parabolic differential equations. A new high order approximation to the Riemann Liouville fractional derivative which is based on the idea of Crank Nicolson method is constructed. High order difference schemes are proposed by using this new high order approximation. The stability analysis of the proposed difference schemes are investigated via three different stability methods. Numerical examples to support the theoretical pretensions about the convergence and stability of the proposed methods are given.

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Produktbeschreibung
This book is devoted to the numerical solution of the fractional parabolic differential equations. A new high order approximation to the Riemann Liouville fractional derivative which is based on the idea of Crank Nicolson method is constructed. High order difference schemes are proposed by using this new high order approximation. The stability analysis of the proposed difference schemes are investigated via three different stability methods. Numerical examples to support the theoretical pretensions about the convergence and stability of the proposed methods are given.
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Autorenporträt
The author obtained her PhD degree in Applied Mathematics in 2016 in Turkey. She is a productive and dedicated researcher with 9 publications in peer-reviewed academic journals, 6 conference proceedings and several book chapter translations. Her research areas are Fractional Partial Differential Equations and Numerical Analysis.