Volume 3 Numerical Methods

Book

Volume 3 Numerical Methods

Edited by: George Em Karniadakis

Part of the multi-volume work

Handbook of Fractional Calculus with Applications

Language: English

Published/Copyright: 2019

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De Gruyter Reference

About this book

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.

A unique, comprehensive overview of fractional calculus and its applications
With authoritative contributions from the world's leading experts
Of interest to mathematicians, physicists, and engineers

Author / Editor information

George Em Karniadakis, Brown University, USA.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	IX
Fundamental approaches for the numerical handling of fractional operators and time-fractional differential equations Kai Diethelm Requires Authentication Unlicensed Licensed	1
Time-fractional derivatives Xuan Zhao and Zhi-Zhong Sun Requires Authentication Unlicensed Licensed	23
High-order finite difference methods for fractional partial differential equations Hengfei Ding and Changpin Li Requires Authentication Unlicensed Licensed	49
Spectral methods for some kinds of fractional differential equations Traditional and Müntz spectral methods Chuanju Xu Requires Authentication Unlicensed Licensed	101
Spectral methods for fractional differential equations using generalized Jacobi functions Jie Shen and Changtao Sheng Requires Authentication Unlicensed Licensed	127
Spectral and spectral element methods for fractional advection–diffusion–reaction equations Anna Lischke, Mohsen Zayernouri and Zhongqiang Zhang Requires Authentication Unlicensed Licensed	157
Discontinuous Galerkin and finite element methods Weihua Deng and Xudong Wang Requires Authentication Unlicensed Licensed	185
Numerical methods for time-space fractional partial differential equations Fawang Liu and Ian Turner Requires Authentication Unlicensed Licensed	209
Comparison of two radial basis collocation methods for Poisson problems with fractional Laplacian Guofei Pang and Wen Chen Requires Authentication Unlicensed Licensed	249
Particle tracking solutions of vector fractional differential equations: A review Yong Zhang and Mark Meerschaert Requires Authentication Unlicensed Licensed	275
Singularities Martin Stynes Requires Authentication Unlicensed Licensed	287
Fast numerical methods for space-fractional partial differential equations Hong Wang Requires Authentication Unlicensed Licensed	307
Fast methods for the computation of the Mittag-Leffler function Roberto Garrappa and Marina Popolizio Requires Authentication Unlicensed Licensed	329
Index Requires Authentication Unlicensed Licensed	347

Publishing information

Pages and Images/Illustrations in book

eBook published on:

April 15, 2019

eBook ISBN:

9783110571684

Hardcover published on:

April 15, 2019

Hardcover ISBN:

9783110570830

Pages and Images/Illustrations in book

Front matter:

10

Main content:

350

Illustrations:

18

Coloured Illustrations:

28

Tables:

20

https://doi.org/10.1515/9783110571684

eBook ISBN: 9783110571684

Hardcover ISBN: 9783110570830

Keywords for this book

Gebrochene Analysis

Audience(s) for this book

Researchers and graduate students in mathematics, physics, and engineering.

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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Volume 3 Numerical Methods

Overview

About this book

Author / Editor information

Topics

Table of contents

Bibliographic data