# NAG FL Interfaced02pjf (ivp_​rk_​interp_​eval)

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## 1Purpose

d02pjf evaluates the interpolant calculated by d02phf, following an integration step performed by d02pgf to solve an initial value problem.

## 2Specification

Fortran Interface
 Subroutine d02pjf ( n, t, sol,
 Integer, Intent (In) :: icheck, n, nwant, ideriv, lwcomm Integer, Intent (Inout) :: iwsav(130), ifail Real (Kind=nag_wp), Intent (In) :: t Real (Kind=nag_wp), Intent (Inout) :: wcomm(lwcomm), rwsav(32*n+350) Real (Kind=nag_wp), Intent (Out) :: sol(nwant)
#include <nag.h>
 void d02pjf_ (const Integer *icheck, const Integer *n, const Integer *nwant, const double *t, const Integer *ideriv, double sol[], double wcomm[], const Integer *lwcomm, Integer iwsav[], double rwsav[], Integer *ifail)
The routine may be called by the names d02pjf or nagf_ode_ivp_rk_interp_eval.

## 3Description

When integrating using the reverse communication Runge–Kutta integrator d02pgf, the solution or its derivatives can be obtained inexpensively between steps by interpolation. d02phf is called after a step by d02pgf 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). d02pjf can then be called to evaluate interpolated approximations of the function or its derivatives at any value of $t$ in the interval $\left({t}_{k-1},{t}_{k}\right)$.

## 4References

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

## 5Arguments

1: $\mathbf{icheck}$Integer Input
On entry: indicates whether consistency checks on input arguments should be performed
${\mathbf{icheck}}\ne 1$
Don't perform checks on input arguments.
${\mathbf{icheck}}=1$
Perform consistency checks on input arguments.
It is recommended to use ${\mathbf{icheck}}=1$ on the first call following a call to d02phf and to set ${\mathbf{icheck}}\ne 1$ on subsequent calls within the last step to avoid the overhead of argument checking.
2: $\mathbf{n}$Integer Input
On entry: $n$, the dimension of the system of ODEs being integrated.
Constraint: this must be the same value as supplied in a previous call to d02pqf.
3: $\mathbf{nwant}$Integer Input
On entry: only the first nwant system components to be computed. This should be the same value as passed to d02phf when computing the interpolant.
Constraint: ${\mathbf{nwant}}={\mathbf{nwant}}$ passed to d02phf.
4: $\mathbf{t}$Real (Kind=nag_wp) Input
On entry: $t$, 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 d02pgf.
5: $\mathbf{ideriv}$Integer Input
On entry:
${\mathbf{ideriv}}=0$
Compute approximations to the first nwant components of the solution $y\left(t\right)$.
${\mathbf{ideriv}}=1$
Compute approximations to the first nwant components of the first derivatives of the solution ${y}^{\prime }\left(t\right)$.
Constraint: ${\mathbf{ideriv}}=0$ or $1$.
6: $\mathbf{sol}\left({\mathbf{nwant}}\right)$Real (Kind=nag_wp) array Output
On exit:
${\mathbf{ideriv}}=0$
The first nwant components of the solution $y\left(t\right)$.
${\mathbf{ideriv}}=1$
The first nwant components of the first derivatives of the solution ${y}^{\prime }\left(t\right)$.
7: $\mathbf{wcomm}\left({\mathbf{lwcomm}}\right)$Real (Kind=nag_wp) array Communication Array
On entry: this must be the same array supplied in a previous call to d02phf. It must remain unchanged between calls.
8: $\mathbf{lwcomm}$Integer Input
On entry: length of wcomm. This should be the same value as supplied in a previous call to d02phf.
If in a previous call to d02pqf:
• ${\mathbf{method}}=1$ or $-1$, lwcomm must be at least $1$.
• ${\mathbf{method}}=2$ or $-2$, lwcomm must be at least ${\mathbf{n}}+\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{n}},5×{\mathbf{nwant}}\right)$.
• ${\mathbf{method}}=3$ or $-3$, ${\mathbf{lwcomm}}\ge 8×{\mathbf{nwant}}$.
9: $\mathbf{iwsav}\left(130\right)$Integer array Communication Array
10: $\mathbf{rwsav}\left(32×{\mathbf{n}}+350\right)$Real (Kind=nag_wp) array Communication Array
On entry: these must be the same arrays supplied in a previous call d02pgf. They must remain unchanged between calls.
On exit: information about the integration for use on subsequent calls to d02pgf, d02phf or other associated routines.
11: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, a previous call to the setup routine 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.
On entry, ${\mathbf{ideriv}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ideriv}}=0$ or $1$.
On entry, ${\mathbf{lwcomm}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{nwant}}=⟨\mathit{\text{value}}⟩$.
Constraint: for ${\mathbf{method}}=-2$ or $2$, ${\mathbf{lwcomm}}\ge {\mathbf{n}}+\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{n}},5×{\mathbf{nwant}}\right)$.
On entry, ${\mathbf{lwcomm}}=⟨\mathit{\text{value}}⟩$.
Constraint: for ${\mathbf{method}}=-1$ or $1$, ${\mathbf{lwcomm}}\ge 1$.
On entry, ${\mathbf{lwcomm}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{nwant}}=⟨\mathit{\text{value}}⟩$.
Constraint: for ${\mathbf{method}}=-3$ or $3$, ${\mathbf{lwcomm}}\ge 8×{\mathbf{nwant}}$.
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$, but the value passed to the setup routine was ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
On entry, ${\mathbf{nwant}}=⟨\mathit{\text{value}}⟩$, but on interpolation setup ${\mathbf{nwant}}=⟨\mathit{\text{value}}⟩$.
Constraint: nwant must be unchanged from setup.
The previous call to the interpolation setup routine returned an error.
You cannot call this routine before you have called the interpolation setup.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

## 7Accuracy

The computed values will be of a similar accuracy to that computed by d02pgf.