Solve Perturbation problem with mathematica

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SUMMARY

The discussion centers on solving a perturbation problem using Mathematica for a thesis in fluid mechanics. The equation presented is u'(1-epsilon(u')^2)=-y, with boundary conditions u0(1)=0 and u1(1)=0. The user has already solved the momentum equation by the perturbation method and seeks assistance in encoding and validating the solution in Mathematica. Clarification on the parameters and functions involved, specifically u, u0, u1, and epsilon, is necessary for further assistance.

PREREQUISITES
  • Understanding of perturbation methods in fluid mechanics
  • Familiarity with Mathematica (MMA) for coding mathematical solutions
  • Knowledge of boundary value problems and their formulations
  • Basic concepts of fluid dynamics and momentum equations
NEXT STEPS
  • Research "Mathematica coding for boundary value problems"
  • Learn about "perturbation methods in fluid mechanics"
  • Explore "Mathematica functions for numerical validation"
  • Study "how to define and manipulate functions in Mathematica"
USEFUL FOR

Mechanical engineers, graduate students in fluid mechanics, and researchers looking to implement perturbation methods in Mathematica for thesis or project work.

Necmi
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u'(1-epsilon(u')^2)=-y
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
 
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Is this homework? In any case, you will probably have to give more details.
 
No its my thesis.İm mechanical engineer.İm doing master on fluid mechanics
 
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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Necmi said:
u'(1-epsilon(u')^2)=-y
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
 
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.
 
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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I would like to send you the solution.How do you want to send.Mail ?
 
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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.
 

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