in 2D on matlab. In Pde>Boundary specify conditions, what do the "q" and "g" coefficients of my equation represent?
This is not a difficult problem to solve. I would proceed this way, I assume c, C and f(x,y) are are given and that c is a constant. I would use the finite difference method for simplicity. As I read x is in [0,H] and I take y in [0,1] for simplicity. I discretise the domain [0,H]x[0,1] as x_1,x_2,....,x_n and y_1,y_2,...y_m. The sought solution u(x,y) is the unknown vector [u(x_1,y_1),u(x1,y2),.... u(x_1,y_m),(x_2,y_1),(x_2,y_2),...,(x_2,y_m),..........,(x_n,y_1),(x_n,y_2),.....,(x_n,y_m)]^T. Now I use a second order scheme and write the equation. At the end one ends up with a trigiadonal matrix. Impose the boundary condition and eliminate a column/row of aforementioned matrix. Now solve the linear system using one of the linear solvers such as an LU decomposition. I hope this helps.
The finite difference relation that you obtain for equation 1 should be like this
-c [ { u(x_i+1,y_j) -2 u(x_i,y_j)+u(x_i-1,y_j)}/dx^2 + { u(x_i,y_j+1) -2 u(x_i,y_j)+u(x_i,y_j_1)}/dy^2}] + beta u(x_i,y_j) = f(x_i,y_j) for i = 2,...n and for j = 1,2,...,m
The Dirichlet boundary condition becomes u(x_1,y_j) = 0 for j=1,...,m
The Neumann boundary condition [u(x_i+1,y_j) -u(x_j-1,j_j)]/2*dx = C u(x_n,y__j) for j = 1,2,...m
You have it all now. You just need to connect the dots.
Cheers.
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