Green's Function: Understanding & Calculation in Matlab

In summary, the user is struggling with calculating displacement using Eshelby's tensor. They are having difficulty with understanding Green's function and need help expressing it in Matlab. They ask for a simple explanation of Green's function and clarify that it is a commonly used technique in physics.
  • #1
graba
8
0
Dear users,

right now I am struggling with calculations of the displacement in the analytically way. I am trying to accomplish this with help of the Eshelby's work (Eshelby's tensor). Right now I have a problem with Green's function. Displacement is expressed by Green's function, it looks like this (please see attachment).
Now I need Your help, because I don't know how to express Green's function from above equation in Matlab. Can anybody explain the Green's function from the simplest mathematical way?
 

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  • #2
I've no clue what are you be talking about :-(. Could you describe which problem you are looking at? Green's functions are a very broad technique used nearly everywhere in physics. So it's hard to guess what you are looking at!
 

FAQ: Green's Function: Understanding & Calculation in Matlab

1. What is the purpose of Green's function?

Green's function is a mathematical tool used to solve differential equations. It provides a way to represent the response of a linear, time-invariant system to an arbitrary input. In other words, it helps us understand the behavior of a system by breaking it down into simpler components.

2. How is Green's function calculated?

Green's function can be calculated using various methods, such as analytical solutions or numerical techniques. In Matlab, the most common method is to use the built-in greenfun function, which calculates the Green's function for a given differential equation and boundary conditions.

3. Can Green's function be used for non-linear systems?

No, Green's function is only applicable to linear systems. This means that the system must follow the principle of superposition, where the response to a sum of inputs is equal to the sum of the responses to each individual input. Non-linear systems do not follow this principle and thus cannot be solved using Green's function.

4. What are the benefits of using Green's function in Matlab?

Using Green's function in Matlab allows for a more efficient and accurate solution to differential equations. It also provides a better understanding of the behavior of a system, as it breaks it down into simpler components. Additionally, Matlab offers various tools and functions for manipulating and visualizing Green's function, making it a powerful tool for scientists and engineers.

5. Can Green's function be used in any type of system?

Yes, Green's function can be used in a wide range of systems, including mechanical, electrical, and thermal systems. However, the system must be linear and time-invariant for Green's function to be applicable.

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