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.