Solving Diff. Eq: p & dp/dx Conditions, Mesh Creation

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Discussion Overview

The discussion revolves around solving a differential equation, specifically focusing on boundary conditions for pressure (p) and its derivative (dp/dx), as well as methods for creating a mesh to facilitate numerical solutions. Participants explore various approaches to tackle the equation, including numerical algorithms and integration techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks methods to solve a differential equation and mentions the need for boundary conditions for p and dp/dx.
  • Another participant suggests that a numeric algorithm may be appropriate for solving the equation and mentions that standard methods could suffice depending on the required accuracy.
  • A third participant questions the use of partial derivative signs in the equation, suggesting that if x is the only variable, it can be integrated directly.
  • One participant expresses a realization of oversimplifying the problem, indicating a need for further exploration and data collection.
  • A later post mentions finding a paper that could help solve the problem but expresses difficulty in understanding the numerical setup and requests assistance with MATLAB coding.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best approach to solve the differential equation, with various methods and interpretations being proposed. The discussion remains unresolved regarding the specific techniques to be employed.

Contextual Notes

There are indications of missing assumptions regarding the variables involved in the differential equation, as well as uncertainties about the numerical methods and integration techniques discussed.

Who May Find This Useful

This discussion may be useful for individuals interested in numerical methods for solving differential equations, particularly in engineering contexts, as well as those seeking to understand boundary conditions and mesh creation in computational applications.

Mad_MechE
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I am trying to solve this differential equation: http://sites.google.com/site/theuntouchableproject/"
I believe i can come up with 2 boundary conditions for p and dp/dx.
i want to create a mesh such that i can solve this equation at different locations that i perscribe. What methods can i use to solve this equation... this is the first time i have ran into an equation of this form.
 
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Hi there Mad MechE,

Your mention of a mesh makes me inclined to think you are asking about the most suitable numeric algorithm to solve the equation, is it the case?

In any case the ODE looks to me rather well behaved and depending on the accuracy you are looking for any standard method would do your purposes.

I attach a copy of the resulst given by the quickest of the alogorithms I know, i.e. just use MathCAD. But any home built algorithm would do the same.

Cheers

Muzialis
 

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Why do you have partial derivative signs on the left side when "x" appears to be the only variable? If there is some other variable, say "y" or "t", since it does not appear in the equation, you can just ignore it.

We can immediately integrate both sides with respect to x to get
[tex]h^3\frac{dp}{dx}= 6U\mu h[/itex] <br /> so<br /> [tex]\frac{dp}{dx}= \frac{6U\mu}{h^2}+ C[/tex]<br /> and, since [itex]h= x_0+ x^2/2R[/itex], that is<br /> [tex]\frac{dp}{dx}= \frac{6U\mu}{(x_0+ x^2/2R)^2}[/tex]<br /> and you just have to integrate, using, I would recommend, "partial fractions".[/tex]
 
I think i may have over simplified the problem... which is good because now i have a baseline for the data i want... later tonight i will write up the problem i am having and upload them!
Thank you all for your help!

MT
 
Alright... i found this paper that has the ability to solve my problem but i don't know any real way about setting it up to do it numerically. I have attached that paper such that it can be referenced to. I read it several times and i don't think i fully comprehend the way the solution was set up. I was hoping that i could produce some MATLAB code to solve the problem but i need to understand it first. Could you please assist me in figuring out what it all means?

Thanks

MT
 

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