An Integral Equation And A Representation For A Greens Function
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Author | : H. H. Kagiwada |
Publisher | : |
Total Pages | : 10 |
Release | : 1967 |
Genre | : |
ISBN | : |
The report discusses a method for representing a Green's function using a Fredholm integral equation for which effective solution methods are known. The final step in the mathematical solution of many problems in mathematical physics and engineering is the solution of a linear two-point boundary differential equation, of which the Green's function provides the solution of interest. Green's functions have been regarded as only of theoretical interest because of the difficulty of computing them. An initial-value method using Hadamard's variational formula was presented in AD-648 654; the present study gives an alternative method in which the differential equations and auxiliary conditions are transformed into integral equations.
Author | : Harriet H. Natsuyama |
Publisher | : |
Total Pages | : 5 |
Release | : 1967 |
Genre | : Green's functions |
ISBN | : |
The report discusses a method for representing a Green's function using a Fredholm integral equation for which effective solution methods are known. The final step in the mathematical solution of many problems in mathematical physics and engineering is the solution of a linear two-point boundary differential equation, of which the Green's function provides the solution of interest. Green's functions have been regarded as only of theoretical interest because of the difficulty of computing them. An initial-value method using Hadamard's variational formula was presented in AD-648 654; the present study gives an alternative method in which the differential equations and auxiliary conditions are transformed into integral equations.
Author | : V. P. Sreedharan |
Publisher | : |
Total Pages | : 96 |
Release | : 1961 |
Genre | : Bessel functions |
ISBN | : |
The domains of analyticity of solutions of the equation delta u! k square times u equals 0 in two independent variables are studied with a view to solving boundary-value problems in the large. The boundary value problems are transformed into function theoretic problems. Specifically the Sommerfeld half-plane problem for delta u! K square times u equals 0 is solved. A related result on integral equations is obtained. Green's functions for a wedge with various boundary conditions are constructed in the case of the equation delta u! k square times u equals 0. (Author).
Author | : Ram P. Kanwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 327 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1461207657 |
This second edition of Linear Integral Equations continues the emphasis that the first edition placed on applications. Indeed, many more examples have been added throughout the text. Significant new material has been added in Chapters 6 and 8. For instance, in Chapter 8 we have included the solutions of the Cauchy type integral equations on the real line. Also, there is a section on integral equations with a logarithmic kernel. The bibliography at the end of the book has been exteded and brought up to date. I wish to thank Professor B.K. Sachdeva who has checked the revised man uscript and has suggested many improvements. Last but not least, I am grateful to the editor and staff of Birkhauser for inviting me to prepare this new edition and for their support in preparing it for publication. RamP Kanwal CHAYfERl Introduction 1.1. Definition An integral equation is an equation in which an unknown function appears under one or more integral signs Naturally, in such an equation there can occur other terms as well. For example, for a ~ s ~ b; a :( t :( b, the equations (1.1.1) f(s) = ib K(s, t)g(t)dt, g(s) = f(s) + ib K(s, t)g(t)dt, (1.1.2) g(s) = ib K(s, t)[g(t)fdt, (1.1.3) where the function g(s) is the unknown function and all the other functions are known, are integral equations. These functions may be complex-valued functions of the real variables s and t.
Author | : William Vernon Lovitt |
Publisher | : |
Total Pages | : 280 |
Release | : 1924 |
Genre | : Integral equations |
ISBN | : |
Author | : Christopher Denis Green |
Publisher | : |
Total Pages | : 260 |
Release | : 1969 |
Genre | : Mathematics |
ISBN | : |
Author | : L. Eskola |
Publisher | : Springer Science & Business Media |
Total Pages | : 203 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401123705 |
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a background in the fundamental field theories that form the basis for various geophysical methods, such as potential theory, electromagnetic theory, and elastic strain theory. A fairly extensive knowledge of mathematics, especially in vector and tensor calculus, is also assumed.
Author | : Yuri A. Melnikov |
Publisher | : Walter de Gruyter |
Total Pages | : 448 |
Release | : 2012-04-02 |
Genre | : Mathematics |
ISBN | : 3110253399 |
Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.
Author | : Yu. A. Melnikov |
Publisher | : Computational Mechanics |
Total Pages | : 296 |
Release | : 1995 |
Genre | : Science |
ISBN | : |
This book is probably the first attempt to make this special topic in the field of partial differential equations accessible to a large audience. The book contains a description of how to construct Green's functions and matrices for elliptic partial differential equations. A number of applications are also presented showing the computational capability of the Green's functions method, and indicate possible ways to put into practice the results of the present study.
Author | : Gary Francis Roach |
Publisher | : |
Total Pages | : 302 |
Release | : 1970 |
Genre | : Mathematics |
ISBN | : |