Method of images to solve green's function problems

In summary, the method of images is a technique used to solve boundary value problems by creating a mirrored image of the given boundary conditions. This allows for a simpler solution by using the Green function and differentiation. However, some may struggle with memorizing the different images for each boundary condition. It is possible to logically work out the solution from the method of images, but it may require some differentiation.
  • #1
pivoxa15
2,255
1
How does the method of images work? I can see why it works (by going back to the form of the Green function and differentiating) but don't see how useful it is
to solve problems. At the moment I am basically memorising the different
images for each boundary condition which I am sure is not the way to go.
How do you think about it so that one can work out the solution logically from the method of images?

Is there a way to work out the solution from the method of images alone without needing to do any differentiation?
 
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Ttt !
 

Related to Method of images to solve green's function problems

What is the Method of Images?

The Method of Images is a mathematical technique used to solve Green's function problems in physics and engineering. It involves creating a mirrored image of the original problem and using it to cancel out certain boundary conditions, simplifying the problem.

When is the Method of Images used?

The Method of Images is often used in electrostatics and fluid dynamics problems, where boundary conditions can be represented by point charges or vortices, making it easier to find solutions.

What are the advantages of using the Method of Images?

The Method of Images offers several advantages, including simplifying complex boundary conditions, reducing the computational effort required to solve a problem, and providing an intuitive understanding of the problem.

Are there any limitations to the Method of Images?

While the Method of Images is a powerful tool, it has some limitations. It can only be used for problems with certain types of boundary conditions, and it may not always provide an accurate solution in cases where the boundary conditions are not well-defined.

How do I apply the Method of Images to a problem?

To apply the Method of Images, you first need to identify the problem's boundary conditions and determine if they can be represented by point charges or vortices. Then, you can create the mirrored images and use them to simplify the problem and find a solution.

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