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

naginterfaces.library.ode.ivp_stiff_nat_interp(xsol, m, comm, neq, x, nqu, hu, h)

ivp_stiff_nat_interp interpolates components of the solution of a system of first-order ordinary differential equations from information provided by the integrators in submodule ode.

For full information please refer to the NAG Library document for d02xj

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/d02/d02xjf.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

$m$, 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.

neqint

The value used for the argument $neq$ when calling the integrator.

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 $1$)

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

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

(errno $1$)

On entry, $m=⟨value⟩$ and $neq=⟨value⟩$.

Constraint: $m\le neq$.

(errno $1$)

On entry, $neq=⟨value⟩$.

Constraint: $neq\ge 1$.

(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 $3$)

On entry, $xsol=⟨value⟩$, $x=⟨value⟩$ and $h=⟨value⟩$.

Constraint: $xsol$ should not be an extrapolation point.

Notes

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

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