# Helmholtz equation

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## Helmholtz equation

[′helm‚hōlts i‚kwā·zhən]
(mathematics)
A partial differential equation obtained by setting the Laplacian of a function equal to the function multiplied by a negative constant.
(optics)
An equation which relates the linear and angular magnifications of a spherical refracting interface. Also known as Lagrange-Helmholtz equation.
(physical chemistry)
The relationship stating that the emf (electromotive force) of a reversible electrolytic cell equals the work equivalent of the chemical reaction when charge passes through the cell plus the product of the temperature and the derivative of the emf with respect to temperature.
References in periodicals archive ?
The differential transform method is used in many fields and many mathematical physical problems such as a system of differential equations [18], a class of time dependent partial differential equations (PDEs) [19], wave, Laplace and heat equations [20], the fractional diffusion equations [21], two-dimensional transient heat flow [22], nonlinear partial differential equations [23], diffusion-convection equation [24], convection-dispersion problem [25], linear transport equation [26], two-dimension transient atmospheric pollutant dispersion [27], Helmholtz equation [28].
We note that expansion (3) holds for the Helmholtz equation outside the simple domain [8, page 31, Lemma 2.
In a Cartesian coordinate system, the 2D Helmholtz equation is
The two-dimensional CLF method provides alternative semi-analytical solutions to the 2D Helmholtz equation.
The 26 papers selected for publication consider such topics as a kind of Riemann boundary value problem for tri-harmonic functions in Clifford analysis, high-frequency asymptotics for the modified Helmholtz equation in a half-plane, positive solutions of singular third-order three-point boundary value problems, the numerical simulation of long-period ground motion on basin effects, and the second fundamental problem of periodic plane elasticity of a one-dimensional hexagonal quasicrystal.
The propagation equation is restricted in the patterned stratified structure to the following Helmholtz equation [17]:
6) Beam Propagation Method (BPM): A numerical analysis technique in electromagnetics for solving the Helmholtz equation under conditions of a time-harmonic wave.
Yiping Fu, Compact Fourth Order Finite Difference Schemes for Helmholtz Equation with High Wave Numbers, J.
The model was solved at first by using one of the most commonly employed algorithms for matrices arising from finite element formulations for the Helmholtz equation (Von Erstoff et al.
mu][epsilon](x) = 1, it is then clear that one is led to deal with the Helmholtz equation.
Many applications in physics deal with the Helmholtz equation in three dimensions.

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