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4.1 Initial Value Problems of First Order

2 guinea pigs will often be used:



(1) Relaxation equation
$\displaystyle \frac{dy}{dt}$ $\textstyle =$ $\displaystyle -\lambda \, y\, , \;\;\; {\rm with} \;\;
y(t=0)=y_{0}$  



(2) Harmonic oscillator in linear form
$\displaystyle \frac{d \mbox{$\bf y$}}{dt}$ $\textstyle =$ $\displaystyle \mbox{${\bf L}$} \cdot \mbox{$\bf y$}\,,\;\;\;\;{\rm where}\;\;
\...
...\begin{array}{cc}0&1\\  \vspace{-9pt}\\  -\omega_{0}^{2}&0\end{array} \right)$}$  



Subsections

Franz J. Vesely Oct 2005
See also:
"Computational Physics - An Introduction," Kluwer-Plenum 2001