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Which equations of elliptic or parabolic type can be taken for visualization?
In addition to the heat equation.
It is necessary to be able to find their numerical solution and deduce all this without much torment using OpenGL.
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So, the heat equation (in a homogeneous medium) is the Laplace equation + the non-stationary term dT / dt, + possibly the source Qv, + different boundary conditions - including, for example, nonlinear ones - such as radiation.
You can add the first derivative to the equation - the type of the equation will change - i.e. get the equation for FAST processes. Well, the truth is that there is still a relaxation parameter that needs to be taken from somewhere.
If you want something beautiful to deduce, take the EQUATION OF OSCILLATIONS.
On the right is the same Laplacian, and on the left is the SECOND derivative with respect to time. And the fluctuations of what exactly this is is already the tenth thing. The solution will be in the form of vibrations - if in color - it turns out very nicely.
Good luck!
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