Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations (Cambridge Monographs on Applied and Computational Mathematics, Series Number 41)

Zayernouri, Mohsen,Wang, Li-Lian,Shen, Jie,Karniadakis, George Em

ISBN 10: 1108490999 / ISBN 13: 9781108490993

Edité par Cambridge University Press, 2024

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N° de réf. du vendeur mon0003734037

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Titre : Spectral and Spectral Element Methods for ...

Éditeur : Cambridge University Press

Date d'édition : 2024

Reliure : hardcover

Etat : Fine

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Synopsis :

This comprehensive introduction to global spectral methods for fractional differential equations from leaders of this emerging field is designed to be accessible to graduate students and researchers across math, science, and engineering. The book begins by covering the foundational fractional calculus concepts needed to understand and model anomalous transport phenomena. The authors proceed to introduce a series of new spectral theories and new families of orthogonal and log orthogonal functions, then present corresponding spectral and spectral element methods for fractional differential equations. The book also covers the fractional Laplacian in unbounded and bounded domains and major developments in time-integration of fractional models. It ends by sampling the wide variety of real-world applications of fractional modeling, including concentration transport in surface/subsurface dynamics, complex rheology and material damage, and fluid turbulence and geostrophic transport.