naginterfaces.library.ode.ivp_​rk_​interp_​eval

naginterfaces.library.ode.ivp_rk_interp_eval(icheck, n, nwant, t, ideriv, comm)

ivp_rk_interp_eval evaluates the interpolant calculated by ivp_rk_interp_setup(), following an integration step performed by ivp_rk_step_revcomm() to solve an initial value problem.

For full information please refer to the NAG Library document for d02pj

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d02/d02pjf.html

Parameters

icheckint

Indicates whether consistency checks on input arguments should be performed

$icheck\ne 1$

Don’t perform checks on input arguments.

$icheck=1$

Perform consistency checks on input arguments.

It is recommended to use $icheck=1$ on the first call following a call to ivp_rk_interp_setup() and to set $icheck\ne 1$ on subsequent calls within the last step to avoid the overhead of argument checking.

nint

$n$, the dimension of the system of ODEs being integrated.

nwantint

Only the first $nwant$ system components to be computed. This should be the same value as passed to ivp_rk_interp_setup() when computing the interpolant.

tfloat

$t$, the value of the independent variable where a solution is desired. Although any value of $t$ can be supplied, accurate solutions can only be obtained for values in the range of the last time-step taken by ivp_rk_step_revcomm().

iderivint

$ideriv=0$

Compute approximations to the first $nwant$ components of the solution $y\left(t\right)$.

$ideriv=1$

Compute approximations to the first $nwant$ components of the first derivatives of the solution $y^{\prime }\left(t\right)$.

commdict, communication object, modified in place

Communication structure.

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

Returns

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

$ideriv=0$

The first $nwant$ components of the solution $y\left(t\right)$.

$ideriv=1$

The first $nwant$ components of the first derivatives of the solution $y^{\prime }\left(t\right)$.

Raises

NagValueError

(errno $1$)

The previous call to the interpolation setup function returned an error.

(errno $1$)

You cannot call this function before you have called the interpolation setup.

(errno $1$)

On entry, $n=⟨value⟩$, but the value passed to the setup routine was $n=⟨value⟩$.

(errno $1$)

On entry, $ideriv=⟨value⟩$.

Constraint: $ideriv=0$ or $1$.

(errno $1$)

On entry, $nwant=⟨value⟩$, but on interpolation setup $nwant=⟨value⟩$.

Constraint: $nwant$ must be unchanged from setup.

(errno $1$)

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

Constraint: for $\text{method}=-3$ or $3$, $\text{lwcomm}\ge 8\times nwant$.

(errno $1$)

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

Constraint: for $\text{method}=-2$ or $2$, $\text{lwcomm}\ge n+max(n,5\times nwant)$.

(errno $1$)

On entry, $\text{lwcomm}=⟨value⟩$.

Constraint: for $\text{method}=-1$ or $1$, $\text{lwcomm}\ge 1$.

(errno $1$)

On entry, a previous call to the setup function has not been made or the communication arrays have become corrupted, or a catastrophic error has already been detected elsewhere.

You cannot continue integrating the problem.

Notes

When integrating using the reverse communication Runge–Kutta integrator ivp_rk_step_revcomm(), the solution or its derivatives can be obtained inexpensively between steps by interpolation. ivp_rk_interp_setup() is called after a step by ivp_rk_step_revcomm() from a previous value of $t$ ($=t_{k-1}$) to its current value, $t=t_k$ (i.e., a $k$th successful time-step has been taken). ivp_rk_interp_eval can then be called to evaluate interpolated approximations of the function or its derivatives at any value of $t$ in the interval $(t_{k-1},t_k)$.

References

Brankin, R W, Gladwell, I and Shampine, L F, 1991, RKSUITE: A suite of Runge–Kutta codes for the initial value problems for ODEs, SoftReport 91-S1, Southern Methodist University