Solve Perturbation problem with mathematica

In summary: My problem statement is as follows: A fluid is flowing through a pipe. A control volume is placed at one end of the pipe and a perturbation to the flow is applied. The perturbation is a nonlinear function of time. The goal is to determine the equilibrium shape of the control volume.
  • #1
Necmi
10
0
u'(1-epsilon(u')^2)=-y
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
 
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  • #2
Is this homework? In any case, you will probably have to give more details.
 
  • #3
No its my thesis.İm mechanical engineer.İm doing master on fluid mechanics
 
  • #4
Can you give even more details? While I may not be the one to be able to help you here, I think that not knowing what ε, u0, u1, etc. represent is going to make it hard for anyone to give you advice.
 
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  • #5
Necmi said:
u'(1-epsilon(u')^2)=-y
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
 
  • #6
I solved the momentum equation of the fluid by perturbation method. I need to encode and validate the solution with mathematica. I used direct expansion in the solution of the perturbation. I want information about the code.
 
  • #7
Which parameters do you know, what is a function of what, what are uo and u1?

You can’t expect help if you don’t explain the problem sufficiently for others to understand it.
 
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  • #8
I would like to send you the solution.How do you want to send.Mail ?
 
  • #9
P_20171116_082718.jpg
P_20171116_082718.jpg
 

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P_20170810_204049.jpg
 

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  • #11
How to my shares data of the problem ?
 
  • #12
I'm still missing the context, but it is nice if you have the solution now.
 
  • #13
Can you use to mathematica?
 
  • #14
So, you solved the problem by hand, but you have to do it in MMA, for your thesis? Is that correct? I know a little MMA, and I'm willing to look into it, but I can't read the photos of your solution, so I'm going to need some more information. Reading your original post, it looks like you are working with 4 functions - u, u0, u1 and epsilon. Is that right? It seems a little peculiar to me. A more explicit problem statement would be helpful.
 
  • #15
Mark Harder said:
So, you solved the problem by hand, but you have to do it in MMA, for your thesis? Is that correct? I know a little MMA, and I'm willing to look into it, but I can't read the photos of your solution, so I'm going to need some more information. Reading your original post, it looks like you are working with 4 functions - u, u0, u1 and epsilon. Is that right? It seems a little peculiar to me. A more explicit problem statement would be helpful.
Thanks.Are you know perturbation method?
Yes its required for my thesis.
 

1. What is perturbation theory?

Perturbation theory is a mathematical method used to approximate solutions to complex problems by breaking them down into simpler, solvable components. It is especially useful for problems that cannot be solved exactly, such as those involving nonlinear systems or small changes to a known solution.

2. How does perturbation theory work?

Perturbation theory works by starting with a known solution to a problem and then introducing a small change or perturbation. The solution is then approximated by considering the perturbation as a small parameter and using a series expansion to find higher-order corrections to the solution. The accuracy of the approximation depends on the size of the perturbation and the number of terms included in the series.

3. What is Mathematica?

Mathematica is a software program used for mathematical and scientific computing. It is particularly well-suited for performing complex calculations, visualizing data, and solving mathematical problems using built-in algorithms and functions. It is commonly used in fields such as physics, engineering, and economics.

4. How can Mathematica be used to solve perturbation problems?

Mathematica has a built-in function called Perturb that can be used to solve perturbation problems. This function takes in the perturbation as a parameter and uses a series expansion to approximate the solution to the problem. It also allows for the inclusion of higher-order corrections and the ability to plot the solution.

5. What are the advantages of using Mathematica for perturbation problems?

One of the main advantages of using Mathematica for perturbation problems is its ability to handle complex calculations and quickly generate accurate solutions. It also has a user-friendly interface and a wide range of built-in functions and algorithms that can be utilized for different types of perturbation problems. Additionally, Mathematica allows for the visualization of solutions, making it easier to interpret and analyze the results.

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