Duffy Mixed Boundary Value Problems

Erscheinungsjahr 2008
ISBN: 978-1-4200-1094-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 488 Seiten

Reihe: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

Methods for Solving Mixed Boundary Value Problems An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations. Straightforward Presentation of Mathematical Techniques The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener–Hopf technique, Green’s function, and conformal mapping. Decipher Mixed Boundary Value Problems That Occur in Diverse Fields Including MATLAB® to help with problem solving, this book provides the mathematical skills needed for the solution of mixed boundary value problems.

Zielgruppe

Applied mathematicians, mathematics students, engineers, and scientists.

Autoren/Hrsg.

Duffy, Dean G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Overview
Examples of Mixed Boundary Value Problem
Integral Equations
Legendre Polynomials
Bessel Functions
Historical Background
Nobili’s Rings
Disc Capicator
Another Electrostatic Problem
Griffith Cracks
The Boundary Value Problem of Reissner and Sagoci
Steady Rotation of a Circular Disc
Separation of Variables
Dual Fourier Cosine Series
Dual Fourier Sine Series
Dual Fourier–Bessel Series
Dual Fourier–Legendre Series
Triple Fourier Sine Series
Transform Methods
Dual Fourier Integrals
Triple Fourier Integrals
Dual Fourier–Bessel Integrals
Triple and Higher Fourier–Bessel Integrals
Joint Transform Methods
The Wiener–Hopf Technique
The Wiener–Hopf Technique When the Factorization Contains No Branch Points
The Wiener–Hopf Technique When the Factorization Contains Branch Points
Green’s Function
Green’s Function with Mixed Boundary Value Conditions
Integral Representations Involving Green’s Functions
Potential Theory
Conformal Mapping
The Mapping z = w + alog(w)
The Mapping tanh[pz/(2b)] = sn(w, k)
The Mapping z = w + ?vw2 - 1
The Mapping w = ai(z - a)/(z + a)
The Mapping z = 2[w - arctan(w)]/p
The Mapping kw sn(w, kw) = kz sn(Kzz/a, kz)
Index