Solving PDE with MATLAB: aFxx+bFx+cFyy+dFy+eFxy=\lambda*F

[ledol83]

hello! does anyone know how to solve the following (like an
eigenvalue) PDE with matlab?

aFxx+bFx+cFyy+dFy+eFxy=\lambda*F

in which i am solving F with certain boundary conditions and
a,b,c,d,e are functions independent of F.

"pdeeig" in MATLAB doesn't seem to be able to handle this, coz of the
annoying Fx and Fy terms :(

thanks so much for any comments & suggestions!

 

[Kummer]

hello! does anyone know how to solve the following (like an
eigenvalue) PDE with matlab?

aFxx+bFx+cFyy+dFy+eFxy=\lambda*F

You can reduce this equation to canonical form using the method of charachteristics by hand, why use Matlab?

 

[ledol83]

it looks the method of characteristics only works for first-order equations, so i really don't know what it going on...

i expected to convert to this format, but it doesn't work coz of the Fx,Fy terms:

-grad.(c*grad(F))+aF=\lambda*d*f

thanks so much for any help!