A Rosenau-type approach to the approximation of the linear Fokker-Planck equation

Giuseppe Toscani

doi:10.3934/krm.2018028

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2018, Volume 11, Issue 4: 697-714. Doi: 10.3934/krm.2018028

This issue Previous Article Preface Next Article Long time strong convergence to Bose-Einstein distribution for low temperature

A Rosenau-type approach to the approximation of the linear Fokker-Planck equation

Giuseppe Toscani

Department of Mathematics, University of Pavia and IMATI-CNR, Pavia, Italy

Received: March 31, 2017

Revised: April 30, 2017

Published: April 2018

This work has been written within the activities of the National Group of Mathematical Physics (GNFM) of INdAM (National Institute of High Mathematics), and partially supported by the MIUR-PRIN Grant 2015PA5MP7 "Calculus of Variations".

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Abstract

The numerical approximation of the solution of the Fokker-Planck equation is a challenging problem that has been extensively investigated starting from the pioneering paper of Chang and Cooper in 1970 [8]. We revisit this problem at the light of the approximation of the solution to the heat equation proposed by Rosenau [25]. Further, by means of the same idea, we address the problem of a consistent approximation to higher-order linear diffusion equations.

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Mathematics Subject Classification: 65M06, 65M12, 82C40, 82D10.

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