The solution of the wave equation
for the corresponding initial and boundary conditions can be found in the following form:
Based on the above derivation, it shows that the cylindrical elastic wave equation
can be equivalent to the plane wave equation
of the one dimensional bar with the linear section area variation.
The longitudinal displacement wave equation
and the transverse displacement wave equation
of a deformation are given respectively by [1, see (196)]
The general equation for fluid motion, the Navier-Stokes equation, is similar to Maxwell's equations and can be used to derive a wave equation
for sound that parallels the wave equation
Abazari: Application of (G'/G)-expansion method to regularized long wave equation
In three-dimensional setting in coordinates x, y, z the wave equation
As a starting point, reference is made to the solution of a one dimensional wave equation
for an elastic string under tension, where hinged boundary conditions at the ends limit the solutions to standing waves in the form of integral numbers of loops.
Our numerical experiments with the wave equation
, described in Section 4, show that the error behavior of both methods strongly depends on the eigenvalues of the correlation matrix.
The Appendix gives the details of the calculation in order to obtain the same solution for both the Wave Equation
(which studies the atomic electron shells) and the Dynamic bi-Laplacian Equation (which studies the atomic nucleus).
Spectraseis has taken things further and implemented the full elastic wave equation
for microseismic data on GPUs.
Global Existence of Generalized Solution to Semi Linear Wave Equation
Pile analysis wave equation
computer program manual.
It is well known that one of the purposes of integral transforms like Fourier, Laplace and Mellin is to solve differential equations like the Heat equation the wave equation
and some EDDs.
Recently, Manocha's research team solved the acoustic wave equation
entirely on GPUs for sound propagation.
y = y(x,t) = a x sin(kx - [omega]t), [m]: wave equation
, considering sinusoidal waves;