scholarly journals Error-Controlled Static Layered-Medium Green’s Function Computation via hp-Adaptive Spectral Differential Equation Approximation Method

2021 ◽  
Vol 11 (9) ◽  
pp. 1329-1342
Author(s):  
Xinbo Li ◽  
Ian Jeffrey ◽  
Mohammed Al-Qedra ◽  
Vladimir I. Okhmatovski
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Approximation Method ◽  
Layered Medium ◽  
Function Computation

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

An integral solution of the electromagnetic seismograph equation

1960 ◽  
Vol 50 (3) ◽  
pp. 461-465
Author(s):  
R. E. Ingram
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Integral Solution ◽  
Ground Movement ◽  
Ground Movements ◽  
Angular Movement ◽  
Electromagnetic Seismograph

ABSTRACT In investigating the response of an electromagnetic seismograph to various ground movements it is advantageous to have the solution of the differential equation as an integral. This is done by finding the Green's function, f(s), for the particular instrument. The angular movement of the galvanometer is then θ(t)=q∫0tf(s)x″(t−s)ds where x(t) is the ground movement and prime stands for the operator d/dt. It is sufficient to find one function, F(s), with dF/ds = f(s), to give the response to a displacement test, a tapping test, or a ground movement.

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