- #1
Green's function for a boundary value problem
- Thread starter Nipon
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In summary, the question is about trying to find an integral that satisfies a boundary value problem, but the result found does not satisfy Green's function. The attempt at a solution is shown in pictures 2 and 3. However, the use of images is not preferred and it is requested to re-post the question using LaTeX notation.
- #2
berkeman
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Welcome to the PF 
@Nipon -- we strongly prefer that you post using LaTeX math notation (see INFO, Help/How-To at the top of the page for a tutorial), but we are rounding up some help for you on this first post of yours. You have shown a lot of effort, which is the primary thing that we look for here. Posting your work in images is problematic for a number of reasons, though, so if you get a chance before there are more replies, it would be great if you could look over the LaTeX tutorial, and add a reply with the problem statement and your work in LaTeX notation. Thanks.
@Nipon -- we strongly prefer that you post using LaTeX math notation (see INFO, Help/How-To at the top of the page for a tutorial), but we are rounding up some help for you on this first post of yours. You have shown a lot of effort, which is the primary thing that we look for here. Posting your work in images is problematic for a number of reasons, though, so if you get a chance before there are more replies, it would be great if you could look over the LaTeX tutorial, and add a reply with the problem statement and your work in LaTeX notation. Thanks.
- #3
berkeman
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Upon further review, we will need this to be re-posted as a new thread using LaTeX notation. Just one example of a problem is what you are trying to say with "G" notation? Please read through the LaTeX tutorial thread and start a new thread with your question. Feel free to send me a message if you have questions about how to post (click on my avatar and select Start a Conversation). Thanks!
Attachments
What is a Green's function for a boundary value problem?
A Green's function for a boundary value problem is a mathematical tool used in solving differential equations with boundary conditions. It represents the solution to the differential equation at a given point in terms of a point source located at a different point.
How is a Green's function for a boundary value problem derived?
A Green's function for a boundary value problem is derived by solving the differential equation with a point source at a specific point and applying the boundary conditions. This results in a solution that can be used to solve the original differential equation for any given set of boundary conditions.
What is the significance of Green's function in solving boundary value problems?
Green's function is significant because it allows us to solve complex differential equations with boundary conditions by breaking them down into simpler problems. It also provides a general solution that can be used for different sets of boundary conditions.
What are the properties of a Green's function for a boundary value problem?
A Green's function for a boundary value problem has several properties, including symmetry, homogeneity, and superposition. These properties make it a powerful tool for solving differential equations with boundary conditions.
How is Green's function used in practical applications?
Green's function has many practical applications, such as in solving heat transfer problems, electromagnetic problems, and fluid flow problems. It is also used in solving problems in quantum mechanics and other fields of physics and engineering.
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