Mixed Boundary Value Problems

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.

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[πz/(2b)] = sn(w, k) The Mapping z = w + λ√w2 - 1 The Mapping w = ai(z - a)/(z + a) The Mapping z = 2[w - arctan(w)]/π The Mapping kw sn(w, kw) = kz sn(Kzz/a, kz) Index