naginterfaces.library.ode.ivp_​stiff_​c1_​interp

naginterfaces.library.ode.ivp_stiff_c1_interp(xsol, m, comm, acor, x, nqu, hu, h)

ivp_stiff_c1_interp interpolates components of the solution of a system of first-order ordinary differential equations from information provided by the integrators in submodule ode. It provides $C^1$ interpolation suitable for general use.

For full information please refer to the NAG Library document for d02xk

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d02/d02xkf.html

Parameters

xsolfloat

The point at which the first $m$ components of the solution are to be evaluated. $xsol$ should not be an extrapolation point, that is $xsol$ should satisfy $(xsol-x)\times hu\le 0.0$. Extrapolation is permitted but not recommended.

mint

The number of components of the solution whose values at $xsol$ are required. The first $m$ components are evaluated.

commdict, communication object

Communication structure populated by a previous call to the integrator.

acorfloat, array-like, shape $\left(\text{neq}\right)$

The value returned in position $(\text{ldysav}+50+\text{i})$, for $\text{i}=1,2,\dots ,\text{neq}$, of the argument $\text{rwork}$ returned by the integrator. If one of the direct communication D02N functions is being employed and ivp_stiff_c1_interp is to be used in $\text{monitr}$, $\text{acor}[\text{i}-1]$ must contain the value given in position $(\text{i},2)$ of the $\text{monitr}$ argument $\text{acor}$, for $\text{i}=1,2,\dots ,\text{neq}$ (e.g., see ivp_stiff_exp_fulljac()).

xfloat

The latest value at which the solution has been computed, as provided in the argument $\text{tcur}$ on return from the optional output ivp_stiff_integ_diag().

nquint

The order of the method used up to the latest value at which the solution has been computed, as provided in the argument $\text{nqu}$ on return from the optional output ivp_stiff_integ_diag().

hufloat

The last successful step used, that is the step used in the integration to get to $x$, as provided in the argument $\text{hu}$ on return from the optional output ivp_stiff_integ_diag().

hfloat

The next step size to be attempted in the integration, as provided in the argument $\text{h}$ on return from the optional output ivp_stiff_integ_diag().

Returns

solfloat, ndarray, shape $\left(m\right)$

The calculated value of the $\text{i}$th component of the solution at $xsol$, for $\text{i}=1,2,\dots ,m$.

Raises

NagValueError

(errno $1$)

The Petzold error test was selected.

(errno $1$)

The BDF integration method is not being used.

(errno $1$)

On entry, $\text{sdysav}=⟨value⟩$ and $nqu=⟨value⟩$.

Constraint: $\text{sdysav}\ge nqu+1$.

(errno $1$)

On entry, $nqu=⟨value⟩$.

Constraint: $nqu\ge 1$.

(errno $1$)

On entry, $\text{neq}=⟨value⟩$ and $\text{ldysav}=⟨value⟩$.

Constraint: $\text{neq}\le \text{ldysav}$.

(errno $1$)

On entry, $m=⟨value⟩$ and $\text{neq}=⟨value⟩$.

Constraint: $m\le \text{neq}$.

(errno $1$)

On entry, $\text{neq}=⟨value⟩$.

Constraint: $\text{neq}\ge 1$.

(errno $1$)

On entry, $\text{ldysav}=⟨value⟩$.

Constraint: $\text{ldysav}\ge 1$.

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 1$.

(errno $2$)

On entry, $hu=0.0$.

(errno $2$)

On entry, $h=0.0$.

Warns

NagAlgorithmicWarning

(errno $3$)

Extrapolation has been performed.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

ivp_stiff_c1_interp evaluates the first $m$ components of the solution of a system of ordinary differential equations at any point using $C^1$ polynomial interpolation based on information generated by the integrator. This information must be passed unchanged to ivp_stiff_c1_interp. ivp_stiff_c1_interp should not normally be used to extrapolate outside the range of values obtained from the above functions.

It may be used with the D02N functions only when the BDF integration method is being employed (setup function ivp_stiff_bdf()), provided the Petzold error test was not selected.