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

Helmholtz equation in given by the following form:

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.