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

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In summary, the conversation is about solving a PDE with MATLAB using the "pdeeig" function, but the Fx and Fy terms seem to be causing issues. The suggestion is to try reducing the equation to canonical form using the method of characteristics. However, it is noted that this method may not work for higher-order equations. The desired format is also mentioned but it cannot be achieved due to the Fx and Fy terms. The person is seeking help and suggestions for solving the PDE.
  • #1
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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  • #2
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?
 
  • #3
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!
 

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

1. What is a PDE?

A PDE, or partial differential equation, is a type of mathematical equation that involves multiple variables and their partial derivatives. It is commonly used to model physical phenomena in fields such as engineering, physics, and economics.

2. How can MATLAB be used to solve PDEs?

MATLAB, or Matrix Laboratory, is a powerful programming language and software tool commonly used in scientific and engineering applications. It has built-in functions and tools specifically designed for solving PDEs, making it a popular choice for researchers and scientists.

3. What is the aFxx+bFx+cFyy+dFy+eFxy=\lambda*F equation used for?

This equation is known as the general linear homogeneous second-order PDE. It can be used to model a wide range of physical phenomena, including heat transfer, wave propagation, and diffusion.

4. What is the significance of the lambda symbol in the equation?

The lambda, or λ, symbol in the equation represents the eigenvalue of the PDE. It is a constant that is determined by the specific problem being solved and plays a crucial role in finding the solution to the PDE.

5. Can MATLAB solve all types of PDEs?

No, MATLAB is not capable of solving all types of PDEs. It is most effective for linear, homogeneous, and second-order PDEs. More complex PDEs may require other numerical methods or specialized software.

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