On entry: values to be used to control step size choice during integration. If any
${\mathbf{CON}}\left(i\right)=0.0$ on entry, it is replaced by its default value described below. In most cases this is the recommended setting.
${\mathbf{CON}}\left(1\right)$, ${\mathbf{CON}}\left(2\right)$, and ${\mathbf{CON}}\left(3\right)$ are factors used to bound step size changes. If the current step size $h$ fails, then the modulus of the next step size is bounded by ${\mathbf{CON}}\left(1\right)\times \left|h\right|$. The default value of ${\mathbf{CON}}\left(1\right)$ is $2.0$. Note that the new step size may be used with a method of different order to the failed step. If the initial step size is $h$, then the modulus of the step size on the second step is bounded by ${\mathbf{CON}}\left(3\right)\times \left|h\right|$. At any other stage in the integration, if the current step size is $h$, then the modulus of the next step size is bounded by ${\mathbf{CON}}\left(2\right)\times \left|h\right|$. The default values are $10.0$ for ${\mathbf{CON}}\left(2\right)$ and $1000.0$ for ${\mathbf{CON}}\left(3\right)$.
${\mathbf{CON}}\left(4\right)$, ${\mathbf{CON}}\left(5\right)$ and ${\mathbf{CON}}\left(6\right)$ are ‘tuning’ constants used in determining the next order and step size. They are used to scale the error estimates used in determining whether to keep the same order of the BDF method, decrease the order or increase the order respectively. The larger the value of
${\mathbf{CON}}\left(\mathit{i}\right)$, for $\mathit{i}=4,5,6$, the less likely the choice of the corresponding order. The default values are: ${\mathbf{CON}}\left(4\right)=1.2$, ${\mathbf{CON}}\left(5\right)=1.3$, ${\mathbf{CON}}\left(6\right)=1.4$.
Constraints:
These constraints must be satisfied after any zero values have been replaced by their default values.
- $0.0<{\mathbf{CON}}\left(1\right)\le {\mathbf{CON}}\left(2\right)\le {\mathbf{CON}}\left(3\right)$;
- ${\mathbf{CON}}\left(\mathit{i}\right)\ge 1.0$, for $\mathit{i}=2,3,\dots ,6$.