The Fractional Laplacian
Autor C. Pozrikidisen Limba Engleză Hardback – 24 feb 2016
- 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
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Specificații
ISBN-13: 9781498746151
ISBN-10: 1498746152
Pagini: 294
Ilustrații: 74
Dimensiuni: 156 x 234 x 23 mm
Greutate: 0.61 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
ISBN-10: 1498746152
Pagini: 294
Ilustrații: 74
Dimensiuni: 156 x 234 x 23 mm
Greutate: 0.61 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Public țintă
Professional Practice & DevelopmentCuprins
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.
Notă biografică
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.
Recenzii
"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
~Daniel Belita, Mathematical Reviews, 2017
Descriere
This book 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. The book covers the fractional Laplacian in one, two, three, and arbitrary dimensions and develops a numerical framework for solving differential equations involving the fractional Laplacian. It presents physical and mathematical concepts as well as detailed mathematical derivations.