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

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The discussion focuses on solving the partial differential equation (PDE) represented as aFxx + bFx + cFyy + dFy + eFxy = λF using MATLAB. Users express difficulty in utilizing the "pdeeig" function due to the presence of the first-order derivatives Fx and Fy. Suggestions include reducing the equation to canonical form, although it is noted that the method of characteristics is typically applicable only to first-order equations, complicating the solution process.

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ledol83
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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!
 
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ledol83 said:
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?
 
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!
 

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