Poisson's equation is a fundamental equation describing the spatial relationship between a certain electron density distribution and the corresponding electric field.

Kang, "A boundary condition capturing method for

Poisson's equation on irregular domains," Journal of Computational Physics, vol.

Given the matter density [rho](x, t), the dynamics of the gravitational field is being determined through

Poisson's equation [[nabla].sup.2][phi] = ([kappa]/2)[rho].

To make the used plasma system equations ((1a), (1b), and (1c)) self-consistent,

Poisson's equation is proceeded as

Thus, the problem of solving (15) is reduced to the problem of solving the following

Poisson's equation:

We can write the divergence of Equation 4 as a form of

Poisson's equation, giving

Poisson's equation is changed into Laplace's equation [[nabla.sup.2][phi] = 0.

In particular, applying normalized systems and Almansi expansions, Karachik studied solutions of some partial equations and some boundary value problems for

Poisson's Equation (see [17,18]).

This calculation leads to solving the

Poisson's equation, which needs models of the source (brain activities) and the head.

Finite difference approximation of

Poisson's equation in polar irregular mesh is defined as

Sweet, "The Fourier and cyclic reduction methods for solving

Poisson's equation," in Handbook of Fluid Dynamics and Fluid Machinery, J.

This equation is shown to lead to

Poisson's equation for a newtonian gravitational potential in the next section.