The Fractional Laplacian

C. Pozrikidis (University of Massachusetts Amherst, USA)

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English

Chapman & Hall/CRC
24 February 2016

Set theory; Applied mathematics

The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional Laplacian explores applications of the fractional Laplacian in science, engineering, and other areas where long-range interactions and conceptual or physical particle jumps resulting in an irregular diffusive or conductive flux are encountered.

Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential equations and integral calculus Clarifies the concept of the fractional Laplacian for functions in one, two, three, or an arbitrary number of dimensions defined over the entire space, satisfying periodicity conditions, or restricted to a finite domain Covers physical and mathematical concepts as well as detailed mathematical derivations Develops a numerical framework for solving differential equations involving the fractional Laplacian and presents specific algorithms accompanied by numerical results in one, two, and three dimensions Discusses viscous flow and physical examples from scientific and engineering disciplines

Written by a prolific author well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science, the book emphasizes fundamental ideas and practical numerical computation. It includes original material and novel numerical methods.

By: C. Pozrikidis (University of Massachusetts Amherst USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 23mm
Weight: 610g
ISBN: 9781498746151
ISBN 10: 1498746152
Pages: 278
Publication Date: 24 February 2016
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

The fractional Laplacian in one dimension. Numerical discretization in one dimension. Further concepts in one dimension. Periodic functions. The fractional Laplacian in three dimensions. The fractional Laplacian in two dimensions. Appendices. References. Index.

Constantine Pozrikidis is a professor at the University of Massachusetts Amherst. He is well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science. He is the author of numerous research papers and books, including the highly recommended Chapman & Hall/CRC books Introduction to Finite and Spectral Element Methods Using MATLAB®, Second Edition; XML in Scientific Computing; Computational Hydrodynamics of Capsules and Biological Cells; Modeling and Simulation of Capsules and Biological Cells; and A Practical Guide to Boundary Element Methods with the Software Library BEMLIB.

Reviews for The Fractional Laplacian

The book under review includes an introductory discussion on the fractional Laplacian which should be accessible to scientists who may not be mathematicians. Practical numerical computations are particularly emphasized, and the book includes many exercises. The fundamental ideas are presented without the traditional organization into theorems and proofs. Here is the list of chapter headings: 1. The fractional Laplacian in one dimension. 2. Numerical discretization in one dimension. 3. Further concepts in one dimension. 4. Periodic functions. 5. The fractional Laplacian in three dimensions. 6. The fractional Laplacian in two dimensions. There are also several appendices: A. Selected de nite integrals. B. The Gamma function. C. The Gaussian distribution. D. The fractional Laplacian in arbitrary dimensions. E. Fractional derivatives. F. Aitken extrapolation of an in nite sum. ~Daniel Belita, Mathematical Reviews, 2017