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How to approach the problem using integral equations and solve it with numerical methods in matlab?

Are there any tutorials with code for begginers?

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2 Answers

You want the Poisson Integral formula, http://en.wikipedia.org/wiki/Poisson_kernel#On_the_unit_disc

It is very likely this is implemented in Matlab already.

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Not sure since I'm just starting in integral equations and have to write the code for numerical solution of the problem to compare it with analytical calculations. I do not know where to start and how to approach it. The good point might be an example with some code to study from –  Chesnokov Yuriy Nov 20 '11 at 13:45
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I think you need to be a bit clearer on what you have done, what precisely you want to do, and where you are stuck for people to give you a genuinely helpful answer.

The following outline may be helpful in reviewing how far you are (the order is not completely fixed). It may be considered a high-level answer for your question on how to approach your problem.

  1. Formulate the problem you want to solve (what is the equation, what is the data that the user should provide, and what is the solution that the program should give?)
  2. Read and understand the numerical method that you will use.
  3. Decide exactly how the user is going to provide the data (the function appearing in the boundary condition) and how the program will provide the solution. For instance, the program may give the value of the solution at some predetermined points - but which points?
  4. Find at least one non-trivial example on which you can test the program.
  5. Think about which steps your program has to take.
  6. One of the steps involves evaluating an integral. Decide how the program will do this.
  7. Translate all this into matlab.
  8. Check that it gives the correct answer on your example.

If you tell us where you are and what you have done then we might be able to help you with the next step. My experience with people without much programming experience is that they often think they are stuck at step 7 (the actual programming). In fact, the steps before that, in which the problem is analysed, are more difficult.

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I'm half in the step 1. Any equation is suitable. e.g. example I need a tutorial where all those steps are explained to solve Dirichlet problem on the unit circle with Fredholm integral equations of the 1st, 2nd kind. –  Chesnokov Yuriy Nov 21 '11 at 13:04
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