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December 23, 2014, 03:56 |
Understanding the mathematical nature of PDE
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#1 |
New Member
West Bengal
Join Date: Dec 2014
Location: Kharagpur
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Hello everyone,
I am fledgling in the domain. I wanted to learn how to identify the mathematical nature of PDE, whether they are hyperbolic/parabolic/elliptic in space and time. I was taught how to make such categorization for a PDE in 2 independent space variables, but how do we go about it when a time derivative is present? And how does understanding the nature of equation and finding characterisitics further help in our errand of solving the equation numerically? I have read some books about it, but I was not able to understand the physical meaning or visualize how exactly the conclusions were drawn Any help would be appreciated. Regards,
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Sachin Shivakumar B.Tech in Mechanical Engineering IIT Kharagpur |
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December 23, 2014, 09:21 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
I suggest using classification by means of eigenvalue analysis. This leads to understand the nature of characteristic curves and classify the PDE |
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December 23, 2014, 14:42 |
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#3 | |
New Member
West Bengal
Join Date: Dec 2014
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Quote:
thanks
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Sachin Shivakumar B.Tech in Mechanical Engineering IIT Kharagpur |
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December 23, 2014, 14:51 |
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#4 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73 |
yes, see the book of Zucrow for examples
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Tags |
characteristics, elliptic, hyperbolic, mathematical analysis, parabolic |
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