We can write the divergence of Equation 4 as a form of Poisson's equation
is changed into Laplace's equation [[nabla.
Finite difference approximation of Poisson's equation
in polar irregular mesh is defined as
This equation is shown to lead to Poisson's equation
for a newtonian gravitational potential in the next section.
Over the past few decades, several kinds of fast methods for solving Poisson's equation
have been proposed.
General Solution of Poisson's Equation
in Stator Slot Subdomain (Region III)
The electric potential is obtained by solving Poisson's equation
with proper boundary conditions, and the magnetic induction is obtained by means of the Biot-Savart law.
The mathematical solution of (9) as Poisson's equation
The thermoelastic displacement function as in  is governed by Poisson's equation
These computational tools, presently successful in the study of plate elasticity, thin and thick plate bending, Poisson's equation
, heat conduction, and piezoelectric materials, are described largely in journals.
Thus, the proposed method is suitable to compute the solution of Poisson's equation
in free space using a multigrid method.
The model requires the solution of two nonlinear partial differential equations -- Poisson's equation
and the continuity equation.