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Integral equations have wide applications in various fields, including continuum mechanics, potential theory, geophysics, electricity and magnetism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control systems, communication theory, mathematical economics, population genetics, queueing theory, and medicine.
Computational Methods for Linear Integral Equations presents basic theoretical material that deals with numerical analysis, convergence, error estimates, and accuracy. The unique computational aspect leads the reader from theoretical and practical problems all the way through to computation with hands-on guidance for input files and the execution of computer programs.
Features:
Offers all supporting Mathematica® files related to the book via the Internet at the authors' Web sites: www.math.uno.edu/fac/pkythe.html or www.math.uno.edu/fac/ppuri.html
Contains identification codes for problems, related methods, and computer programs that are cross-referenced throughout the book to make the connections easy to understand
Illustrates a how-to approach to computational work in the development of algorithms, construction of input files, timing, and accuracy analysis
Covers linear integral equations of Fredholm and Volterra types of the first and second kinds as well as associated singular integral equations, integro-differential equations, and eigenvalue problems
Provides clear, step-by-step guidelines for solving difficult and complex computational problems
This book is an essential reference and authoritative resource for all professionals, graduate students, and researchers in mathematics, physical sciences, and engineering. Researchers interested in the numerical solution of integral equations will find its practical problem-solving style both accessible and useful for their work.
Inhaltsverzeichnis
Preface
Notation
Introduction
Eigenvalue Problems
Equations of the Second Kind
Classical Methods for FK2
Variational Methods
Iteration Methods
Singular Equations
Weakly Singular Equations
Cauchy Singular Equations
Sinc-Galerkin Methods
Equations of the First Kind
Inversion of Laplace Transforms
A. Quadrature Rules
B. Orthogonal Polynomials
C. Whittaker's Cardinal Functions
D. Singular Integrals
Bibliography
Subject Index
Bericht
"The monograph is devoted to numerical methods for solving one-dimensional linear integral equations. Fredholm and Volterra integral equations of first and second kinds are considered. The authors pay more attention to computational aspects of solving integral equations. A lot of numerical examples and results of computations by computers are presented." Mathematical Reviews "This book presents numerical methods and computational aspects for linear integral equations that appear in various areas of applied mathematics, physics, and engineering . The book is an excellent reference for graduate students and researchers in mathematics and engineering." Memoriile Sectiilor Stiintifice
