Page 72 - Process Modelling and Simulation With Finite Element Methods

FEMUB and the Basics of Numerical Analysis 59

Furthermore, the eigenvectors can be interpreted the same way:
>>COl2=V( : ,2) ;
>>plot (xs, co12 (idx) ;
)
(
>>COl3=V : ,3) ;
)
>>plot (xs, co13 (idx) ;
It should be noted that in the case of the Neumann solution, any constant
value can be added to the solution and it will remain a solution. The eigenvectors
are not normalized, so they can be multipled by any number and still be
eigenvectors. Figures 1.8 and 1.9 show the two eigenpairs with largest
eigenvalues in magnitude.

1.6 Summary
This chapter has illustrated that FEMLAB is constructed upon four standard
methods in numerical analysis: root finding, numerical integration by marching
methods, numerical integration for BVPs, and linear systems theory. These tools
are conducive to solving many common problems that arise in chemical
engineering applications in 0-D and 1-D spaces. In the next chapter, we will
begin to see applications where FEMLAB solutions have value added over the
standard solution techniques in 2-D.

References
1. Cutlip M.B. and Shacham M., 2
with Numerical Methods, Prentice-Hall, Upper Saddle River, NJ, 1999.
2. Gear W.C., Numerical Initial Value Problems in Ordinary Differential
Equations, 1971.
3. Golub G.H. and Van Loan C.F., Matrix Computations, 3rd ed. - Baltimore;
London: Johns Hopkins University Press, 1996.
4. Hanselman D. and Littlefield B.,Mastering MATLAB 6: A comprehensive
tutorial and reference, Prentice Hall, Saddle River NJ, 2001.
5. Zimmerman W.B., “On the resistance of a spherical particle settling in a tube
of viscous fluid” Submitted to SIAM J. Applied Maths, 2002.