naginterfaces.library.ode.ivp_​2nd_​rkn_​interp

naginterfaces.library.ode.ivp_2nd_rkn_interp(t, y, yp, nwant, twant, comm)

ivp_2nd_rkn_interp interpolates components of the solution of a non-stiff system of second-order differential equations from information provided by the integrator ivp_2nd_rkn(), when the low-order method has been used.

For full information please refer to the NAG Library document for d02lz

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d02/d02lzf.html

Parameters

tfloat

$t$, the current value at which the solution and its derivative have been computed (as returned in argument $t$ on output from ivp_2nd_rkn()).

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

The $\text{i}$th component of the solution at $t$, for $\text{i}=1,2,\dots ,\text{neq}$, as returned from ivp_2nd_rkn().

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

The $\text{i}$th component of the derivative at $t$, for $\text{i}=1,2,\dots ,\text{neq}$, as returned from ivp_2nd_rkn().

nwantint

The number of components of the solution and derivative whose values at $twant$ are required. The first $nwant$ components are evaluated.

twantfloat

The point at which components of the solution and derivative are to be evaluated. $twant$ should not normally be an extrapolation point, that is $twant$ should satisfy

$$\text{told}\le twant\le t\text{,}$$

or if integration is proceeding in the negative direction

$$\text{told}\ge twant\ge t\text{,}$$

where told is the previous integration point which is held in an element of the array $comm$[‘rwork’] and is, to within rounding, $t-\text{hused}$. ($\text{hused}$ is given by ivp_2nd_rkn_diag().) Extrapolation is permitted but not recommended, and $errno$ = 2 is returned whenever extrapolation is attempted.

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by a prior call to ivp_2nd_rkn_setup().

Returns

ywantfloat, ndarray, shape $\left(nwant\right)$

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

ypwantfloat, ndarray, shape $\left(nwant\right)$

The calculated value of the $\text{i}$th component of the derivative at $t=twant$, for $\text{i}=1,2,\dots ,nwant$.

Raises

NagValueError

(errno $1$)

On entry, $\text{neq}=⟨value⟩$, but in a previous call to the setup function $\text{neq}=⟨value⟩$.

(errno $1$)

The integrator function ivp_2nd_rkn() has not been called.

(errno $1$)

No successful steps, interpolation impossible at $twant=⟨value⟩$.

(errno $1$)

On entry, $nwant=⟨value⟩$.

Constraint: $nwant\ge 1$.

(errno $1$)

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

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

(errno $3$)

Interpolation is not permitted on data from the high order formulas.

Warns

NagAlgorithmicWarning

(errno $2$)

Extrapolation at $twant=⟨value⟩$.

Notes

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

ivp_2nd_rkn_interp evaluates the first $nwant$ ($\le \text{neq}$) components of the solution of a non-stiff system of second-order ordinary differential equations at any point using a special Runge–Kutta–Nystrom formula (see Dormand and Prince (1986)) and information generated by ivp_2nd_rkn() when the low-order method has been used. This information must be presented unchanged to ivp_2nd_rkn_interp. ivp_2nd_rkn_interp should not normally be used to extrapolate outside the range of the values from ivp_2nd_rkn().

References

Dormand, J R and Prince, P J, 1986, Runge–Kutta–Nystrom triples, Mathematical Report TP-CS-86-05, Teesside Polytechnic