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

naginterfaces.library.ode.ivp_rk_interp_setup(irevcm, nwant, yp, comm)

ivp_rk_interp_setup is a reverse communication function that computes the interpolant for evaluation by ivp_rk_interp_eval() anywhere on an integration step taken by ivp_rk_step_revcomm(). The direct communication version of the ivp_rk_interp_setup and ivp_rk_interp_eval() pair is ivp_rkts_interp(). A significant difference in functionality between the forward and reverse communication versions is that ivp_rk_interp_setup and ivp_rk_interp_eval() can interpolate for the high-order Runge–Kutta method.

For full information please refer to the NAG Library document for d02ph

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d02/d02phf.html

Parameters

irevcmint

On initial entry: $irevcm$ must be set to zero to indicate that the interpolant for a new step is being taken.

On intermediate entry: $irevcm$ should remain unchanged.

nwantint

The number of components of the solution to be computed. The first $nwant$ components are evaluated.

ypfloat, array-like, shape $\left(n\right)$

On initial entry: need not be set.

On intermediate entry: $yp$ must contain the values of the derivatives $y_i^{\prime }$ for the given values of the parameters $t$, $y_i$.

commdict, communication object, modified in place

Communication structure.

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

Returns

irevcmint

On intermediate exit: $irevcm$ returns a value $1$ to indicate that a function evaluation is required prior to re-entry; the value of the derivatives must be returned in $yp$ where the value of $t$ is supplied in $t$ and the values $y\left(t\right)$ are supplied in the array $y$.

On final exit:

$irevcm=-1$

Successful exit; $comm$[‘rwsav’] and $comm$[‘wcomm’] contain details of the interpolant.

$irevcm=-2$

Error exit; $\text{errno}$ should be interrogated to determine the nature of the error.

tfloat

On intermediate exit: $t$ contains the value of the independent variable $t$ at which the derivatives $y^{\prime }$ are to be evaluated.

On final exit: contains no useful information.

yfloat, ndarray, shape $\left(n\right)$

On intermediate exit: $y$ contains the value of the solution $y$ at which the derivatives $y^{\prime }$ are to be evaluated.

On final exit: contains no useful information.

Raises

NagValueError

(errno $1$)

You cannot call this function after the integrator has returned an error.

(errno $1$)

You cannot call this function before you have called the step integrator.

(errno $1$)

You cannot call this function after the range integrator has been called.

(errno $1$)

On entry, $n=⟨value⟩$, but the value passed to the setup function was $\text{n}=⟨value⟩$.

(errno $1$)

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

Constraint: $1\le nwant\le n$.

(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

ivp_rk_interp_setup and its associated functions (ivp_rk_step_revcomm(), ivp_rk_interp_eval(), ivp_rkts_setup(), ivp_rkts_reset_tend(), ivp_rkts_diag() and ivp_rkts_errass()) solve the initial value problem for a first-order system of ordinary differential equations. The functions, based on Runge–Kutta methods and derived from RKSUITE (see Brankin et al. (1991)), integrate

$$y^{\prime }=f(t,y)\text{given}y\left(t_0\right)=y_0$$

where $y$ is the vector of $\text{n}$ solution components and $t$ is the independent variable.

ivp_rk_step_revcomm() computes the solution at the end of an integration step. Using the information computed on that step ivp_rk_interp_setup computes the interpolant which can be evaluated at any point on that step by ivp_rk_interp_eval(). If $\text{method}=1$ or $-1$ then there is enough information available from the stages of the last step to provide an interpolant of sufficient order of accuracy; no further derivative evaluations will, therefore, be requested. If $\text{method}=2$ or $-2$ then the interpolant is an order $8$ continuous Runge–Kutta process that requires a further $3$ stages of derivative evaluations that will be requested in turn before a final exit. If $\text{method}=3$ or $-3$ was specified in the call to setup function ivp_rkts_setup() then the interpolant is a continuous Runge–Kutta process requiring a further $7$ stages of derivative evaluations that will be requested in turn.

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