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Poisson's equation

  1. Mar 20, 2012 #1
    I have a problem solving poisson equation in finite difference method using matlab.

    the equation is (δ^2 φ)/(δx^2 )=(-ρ/ϵ N(x))

    where N(x)= a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
  2. jcsd
  3. Mar 20, 2012 #2
    Is this written correctly?
    [tex] \frac{\partial}{\partial x} \left( \frac{\partial \psi}{\partial x} \right)=\frac{- \rho}{\varepsilon} N\left( x \right) [/tex]
    Is this equation in cartesian coordinates, or spherical or cylindrical coordinates? Is N(x) in the numerator?
  4. Mar 20, 2012 #3
    it is in cartesian coordinate.I have to solve in 1Dimention. N(x) is in numerator and it is the doping concentration which is a Gaussian in nature
  5. Mar 20, 2012 #4
    Is this true (i.e., 1-D Poisson equation); with N(x) being a function of x only?
    [tex]-d \left( \frac{\partial \psi}{\partial x} \right)= d E_x (x) =\frac{+ \rho}{\varepsilon} N\left( x \right) dx[/tex]
    Then can't you integrate both sides and put in boundary conditions?
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