# Download Computational Partial Differential Equations: Numerical by Hans Petter Langtangen (auth.) PDF

By Hans Petter Langtangen (auth.)

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Extra info for Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

Sample text

This is done by the call A. factLUO. 1 values must be computed and 7. The difference between the u~ and reported. 2. Steady 1D Heat Conduction 21 u7- 1 = uf, i = 1, ... , n, such that we are ready for a new 8. We must set iteration. 9. A while loop must be wrapped around the linear system generation and the actions 6, 7, and 8. 10. 19) can be reported, if an analytical solution to the problem is available. Before starting the implementation, we should have a test example with exact solution. 30) and apply u(O) = 0 and u'(l) = 1 to find that u(x) = (m + 1)x 1 /(m+1).

The next step is to express T in terms of the unit vectors i and j. 2 we see that T(x) = T(x) cos e(x) i + T(x) sin e(x)j, where T is the magnitude of T. 36) e( x ps 8 2U2 8t . , . 2). 37), after division by h, has the limit equation 8 8x (Tsin e) = e(x) (. 3. 42) This is a nonlinear PDE because the primary unknown u enters in products with itself or its derivatives 10 . Vibrations of astring are normally recognized as being small. Therefore we expect that (8u/8x)2 is small compared with unity.

For exampIe, in the demo program listed in the preceding section, we used casename to initialize the plotfile object, which then ensures that all the plot files have names containing casename. Sometimes you will prefer to have all the casename-related files in a separate directory. The command-line option --casedir mydir to app creates a subdirectory mydir, which is used as current working directory during the simulation. 3 To clean up all files generated by a computer experiment, you can use the Diffpack script RmCase with the casename as argument.