naginterfaces.library.ode.ivp_​adams_​interp

naginterfaces.library.ode.ivp_adams_interp(neqf, twant, nwant, comm)

ivp_adams_interp interpolates components of the solution of a non-stiff system of first-order differential equations from information provided by the integrator functions ivp_adams_roots() or ivp_adams_roots_revcom().

For full information please refer to the NAG Library document for d02qz

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/d02/d02qzf.html

Parameters

neqfint

The number of first-order ordinary differential equations being solved by the integration function. It must contain the same value as the argument $neqf$ in a prior call to the setup function ivp_adams_setup().

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

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

or if integration is proceeding in the negative direction

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

where $\text{told}$ is the previous integration point and is, to within rounding, $\text{tcurr}$ – $\text{hlast}$ (see ivp_adams_diag()). Extrapolation is permitted but not recommended and $errno$ = 2 is returned whenever extrapolation is attempted.

nwantint

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

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by prior calls to ivp_adams_setup() and one of ivp_adams_roots() or ivp_adams_roots_revcom().

Returns

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

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

Raises

NagValueError

(errno $1$)

On entry, $nwant=⟨value⟩$.

Constraint: $nwant\ge 1$.

(errno $1$)

On entry, $nwant=⟨value⟩$ and $neqf=⟨value⟩$.

Constraint: $nwant\le neqf$.

(errno $1$)

On entry, $neqf=⟨value⟩$ and $\text{neqf}=⟨value⟩$ in ivp_adams_setup().

Constraint: $neqf=\text{neqf}$ in ivp_adams_setup().

(errno $1$)

Neither of the appropriate two integrator functions has been called.

Warns

NagAlgorithmicWarning

(errno $1$)

No successful steps had been taken, so interpolation is impossible at $twant=⟨value⟩$.

(errno $2$)

Extrapolation performed at $twant=⟨value⟩$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

ivp_adams_interp evaluates the first $nwant$ components of the solution of a non-stiff system of first-order ordinary differential equations at any point using the method of Watts and Shampine (1986) and information generated by ivp_adams_roots() or ivp_adams_roots_revcom(). ivp_adams_interp should not normally be used to extrapolate outside the current range of the values produced by the integration function.

References

Watts, H A and Shampine, L F, 1986, Smoother interpolants for Adams codes, SIAM J. Sci. Statist. Comput. (7), 334–345