Computational Methods for Linear Integral Equations

ISBN-13: 9781461266129 / Angielski / Miękka / 2012 / 508 str.

Prem Kythe; Pratap Puri

Opis

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover- ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag- netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys- tems, communication theory, mathematical economics, population genetics, queue- ing theory, and medicine. Most of the boundary value problems involving differ- ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Recenzje

"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

Spis treści

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