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From: Bhawas on 3 May 2010 15:36
Hello everyone,
I am trying to solve one and two dimensional Boussinesq equations for groundwater dynamics using implicit finite difference method. I am new to MATLAB and programming so any help to my problem is highly appreciated. Below is the the equation I am trying to solve.

dy/dt = a*d/dx(ydy/dx) + a*d/dz(ydy/dx)

I have wrote this as the follwing finite difference equation
One dimensional
y(t,x) = y(t+1,x) - dt*a*y(t+1,x)*(y(t+1,x-1) - 2*y(t+1,x) + y(t+1,x+1)/dx^2) + (y(t+1,x-1) - y(t+1,x-1)/2*dx)^2

I need to get the numerical solution for the case of constant y ( which is smaller than y at the center of the at the field) boundaries.

I would highly appreciate it If some one could give me some idea on writing the matlab script to solve this difference equation.
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Next: Minimization of multivariate function to estimate parameters