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Example 4

The following nonlinear stiff system has also been solved by the TKSL/386:

$y_1'=-0.04*y_1+10000*y_2*y_3\hspace{3.7cm} y_1(0)=1 \hfill(38)$

$y_2'=0.04*y_1-10000*y_2*y_3-30000000*y_2\hspace{1.1cm}y_2(0)=0 \hfill(39)$

$y_3'=30000000*y_2*y_2\hspace{5.4cm}y_3(0)=0 \hfill(40)$

For a nonlinear system of differential equations the eigenvalues are given by the Jacobi matrix J . In nonlinear systems of differential equations the eigenvalues of the matrix J depend on the time t and they change during the integration. The system above describes fast chemical reactions.

The results are in Fig.11.6. It is typical of the system (38),(39),(40) that SUMA=1 in the entire time interval ( SUMA=y1+y2+y3).


 
Figure 11.6:
\begin{figure}\begin{center} \epsfig{file=stif_n1.eps, height=8.3cm, width=12cm}\end{center}\end{figure}