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