# Poisson's equation

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## Poisson's equation

[pwä′sōnz i‚kwā·zhən]
(mathematics)
The partial differential equation which states that the Laplacian of an unknown function is equal to a given function.
References in periodicals archive ?
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.

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