Solving Poisson's Equation in Finite Difference Method with Matlab

[indrani]

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)

 

[Bob S]

Is this written correctly?
$$\frac{\partial}{\partial x} \left( \frac{\partial \psi}{\partial x} \right)=\frac{- \rho}{\varepsilon} N\left( x \right)$$
Is this equation in cartesian coordinates, or spherical or cylindrical coordinates? Is N(x) in the numerator?

 

[indrani]

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

 

[Bob S]

Is this true (i.e., 1-D Poisson equation); with N(x) being a function of x only?
$$-d \left( \frac{\partial \psi}{\partial x} \right)= d E_x (x) =\frac{+ \rho}{\varepsilon} N\left( x \right) dx$$
Then can't you integrate both sides and put in boundary conditions?