From: "M. Philippe Viredaz" Newsgroups: sci.math.num-analysis Subject: Re: Green's function Date: Mon, 7 Dec 1998 20:13:06 +0100 Green's Function "The Green' s function in the time domain is defined as the displacement as a function of time u(t) at a point, called the receiver, located at a distance a from the disk, the source (Fig. A-1), which is excited at time = 0 by a unit-impulse force P0- The motion of the receiver at time t wiIl have originated earlier at the source, at the retarded time t - a/c, with c = the appropriate wave velocity. Futhermore, the amplitude will have diminished after traveling the distance a. Thus the Green' s function may be denoted as u(t) = g (a, t - a/c). The first argument specifies the spatial distance from the source, the second argument the appropriate retarded time at the source." (p. 366) WOLF; John P.; (1994); Foundation Vibration Analysis Using Simple Physical Models; PTR Prentice Hall, Inc. - Englewood Cliffs, NJ 07632. See also : WHITE; J.E.; (1983); Underground Sound - Application of Seismic Waves; Elsevier - Amsterdam. Good luck! phv. Man J a écrit dans le message <74gskh$494$1@hfc.hk.super.net>... >Dear Friends, > >Anyone who have any idea on " Green's Function " ??? ============================================================================== From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) Newsgroups: sci.math.num-analysis Subject: Re: Green's function Date: 7 Dec 1998 12:31:43 -0500 In article <366BF963.A700BC3F@tuwien.ac.at>, Dietmar Trummer wrote: :Man J wrote: : :> Dear Friends, :> :> Anyone who have any idea on " Green's Function " ??? : :This is part of the theory of (second order) diff equations, especially :of the socalled :Sturm-Liouville-equations. :It also has connections to the theory of distributions. :Maybe you should read a good book on this topic. [...] One can extend this to any order differential equation. In one variable, one has a linear differential problem L(y)=f where L is a differential operator, such as L(y)(x) = sum[j=0 to n] a_j(x) * y^(j)(x) with homogeneous boundary conditions (B.C.) at the endpoints of an interval [A,B], With this lengthy preamble, a Green function corresponding to L and the B.C. is a function G(x,s) such that the problem L(y) = f with given B.C.'s has solution y(x) = integral[A to B] G(x,s) * f(s) ds. Example: Check that the problem (with f to be supplied later) (1/2)*y''= f, y(0) + y(1) = y'(1), y'(0) + y'(1) = 0 has Green's function G(x,s) = abs(x - s). Good luck, ZVK(Slavek). ============================================================================== From: kfroenigk@mmm.com (Karl Roenigk) Newsgroups: sci.math.num-analysis Subject: Re: Green's function Date: Tue, 08 Dec 1998 09:22:55 -0600 an excellent reference is.. "Green's Functions and Boundary Value Problems" Ivar Stakgold, John Wiley & Sons 1979. ISBN 0-471-81967-0 Adequately fundamental, many practical applications... Man J wrote: > Dear Friends, > > Anyone who have any idea on " Green's Function " ??? Opinions expressed herein are my own and may not represent those of my employer. ==============================================================================