Numerical Solution of Integral Equations
Matematika, statistika i informatika
089897
Oxford
1974
16×24
tvrdi s omotom
339
engleski
Cijena: 40,00 EUR
This scholarly work in the field of applied mathematics and numerical analysis is based on materials presented at the joint Liverpool–Manchester Summer School held in July 1973. The book provides a highly important historical and professional overview of the methods and theoretical background in the numerical solution of integral equations, bringing together the papers of leading experts from the Department of Computational and Statistical Science at the University of Liverpool and the Department of Mathematics at the University of Manchester. The structure of this comprehensive volume is divided into three strictly defined sections spanning a total of 25 chapters. Part I (Chapters 1–5) covers the necessary mathematical preliminaries, function spaces, and approximation theory in numerical analysis. Part II (Chapters 6–18) deals in detail with the principal numerical methods for various types of equations, covering direct approaches and quadrature formulae for Fredholm equations of the second kind, variational and Galerkin methods, eigenvalue problems, the stability of step-by-step methods for Volterra equations of the first and second kinds, nonlinear problems, and the analysis of convergence and error estimation. Part III (Chapters 19–25) is dedicated to practical fields of application of integral equations in physics and engineering, with a particular emphasis on potential theory, wave motion, scattering in quantum mechanics, conformal mapping, and the application of the finite element method to the Helmholtz equation. Each chapter is accompanied by an extensive list of references and a summary of recent research of that era, making the book an invaluable historical source for studying the development of computational mathematics.
