Poisson’s Equation

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Post Date September 18, 2009
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How to Solve Poisson’s Equation

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A detailed tutorial on the solving of Poisson’s Equation. Step by step tutorial including several examples of how to solve Poisson’s Equation for reference.

 

 

 

 

 

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Poisson’s Equation is a partial differential equation. It is used in sections of math that deal with engineering and physics. The formula is named after Siméon-Denis Poisson. There are a few different ways of expressing it. In general terms, this equation is expressed as: \Delta\varphi=f

However, in certain branches of math, it is written as {\nabla}^2 \varphi = f..

A third way of expressing it is used in Cartesian coordinates, and it is written as:

\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} \right)\varphi(x,y,z) = f(x,y,z).
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