Boundary Problems and Green's Functions for Linear Differential and Difference Equations

1911 ◽  
Vol 13 (1/4) ◽  
pp. 71 ◽  
Author(s):  
Maxime Bocher
Keyword(s):  
Difference Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Problems ◽  
Linear Differential

Sign Properties of Green's Functions For Two Classes of Boundary Value Problems

1987 ◽  
Vol 30 (1) ◽  
pp. 28-35 ◽  
Author(s):  
P. W. Eloe
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Difference Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Partial Derivatives

AbstractLet G(x,s) be the Green's function for the boundary value problem y(n) = 0, Ty = 0, where Ty = 0 represents boundary conditions at two points. The signs of G(x,s) and certain of its partial derivatives with respect to x are determined for two classes of boundary value problems. The results are also carried over to analogous classes of boundary value problems for difference equations.

Indefinite Green's Functions and Elementary Solutions

1963 ◽  
Vol 6 (1) ◽  
pp. 71-103 ◽  
Author(s):  
G. F. D. Duff ◽  
R. A. Ross
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Applied Mathematics ◽  
Integral Transforms ◽  
Source Distribution ◽  
Asymptotic Estimates ◽  
Elementary Functions ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Superposition Of Solutions

Linear differential equations both ordinary and partial are often studied by means of Green's functions. One reason for this is that linearity permits superposition of solutions. A Green's function describes the "effect" of a point source, and the description of line, surface, or volume sources is achieved by superposing, that is to say, integrating, this function over the source distribution.For equations with constant coefficients the use of integral transforms permits the calculation of such source functions in the form of integrals. Only in the simplest cases is explicit evaluation by elementary functions possible, and this has perforce led to the use of asymptotic estimates, which so thoroughly pervade the domain of applied mathematics.

Sign in / Sign up

Export Citation Format

Share Document