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Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations
出版済み 3-5週間でお届けいたします。
分数常微分方程式および偏微分方程式のためのスペクトル法およびスペクトル要素法 Series: Cambridge Monographs on Applied and Computational Mathematics Author: Zayernouri, Mohsen (Michigan State University) / Wang, Li-Lian (Nanyang Technological University, Singapore) / Shen, Jie (Eastern Institute of Technology, Ningbo, China) / Karniadakis, George Em (Brown University, Rhode Island) Publisher: Cambridge University Press ISBN: 9781108490993 Cover: HARDCOVER Date: 2024年11月 DESCRIPTION 分数モデリングは、数学、科学、工学における高忠実度予測モデリングアプローチの新しいフロンティアです。大学院生と研究者向けのこの入門書は、複雑なレオロジー、時効材料、乱流の扱いやすいモデルとして分数微分方程式を数値的に解くためのガイドです。 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. * Equips students and researchers from diverse backgrounds to use widely applicable models and keep up with an active research area * Explains the research of the authors themselves, who are pioneers of the field * Puts new methods in context with historical asides TABLE OF CONTENTS 1. Fractional calculus and anomalous transport 2. Spectral expansions and related approximations 3. Global schemes for fractional ODEs (FODEs) 4. Global schemes for fractional PDEs (FPDEs) 5. Integral fractional Laplacian in unbounded domains 6. Fractional Laplacian in bounded domains 7. Time-integration of fractional models 8. Applications of anomalous transport and fractional modeling References Index.
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