using time as a variable to classify a pde
Hello Dear friends
I have a problem with classifying PDEs which is I don't know when to use 'time' as a variable for classifying the equations! I would be grateful if I can find the answer of my question as soon as possible. thanks alot |
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is there anyone?
Isn't there anyone who can help me about the so-called problem?
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Thanks for your reply. I have studied Hoffman's CFD book, sometimes it uses only the coefficient matrix of d/dx to define the type of equation and somewhere else it uses the coefficient of time derivative either. for example in equation du/dt+a du/dx=0 , should i use time coefficient to determine the equation type?
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Classification is done for PDE of the type: a(x1,...xn,f,..)*d2f/dx1^2 + ..... = 0 For example in a 2D case the PDE a* d2f/dx1^2 + b * d2f/dx1dx2 + c*d2f/dx2^2 =0 can be classified by analysing the characteristic curves. That can be found in many textbook. If am right, you can see the Hirsch book that uses the eigenvectors analysis |
thank you so much, I will read the book.
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another problem
here is what I got :if 'time' derivative is of the highest order in a equation I have to use it's coefficients in chlassifying the equation or sytem of equation. am I right? for example in the following system
du/dt+a du/dx+b dv/dx=0 dv/dt+c du/dx+ d du/dx=0 but there is another question here: if we have a system like this:. du/dt+a du/dx+b dv/dy=0 dv/dt+c du/dx+ d du/dy=0 here we have 3 variables but as I studied in different books we just use d/dx and d/dy coefficient matrixes to classify the equation. |
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You can use a matrix form of the system to write du/dt + A. du/dx+B. du/dy = 0 use u= uk*exp(i k.x) and develep an aigenvalue analysis |
thank you so much.
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