NAG FL Interfaced02prf (ivp_​rkts_​reset_​tend)

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1Purpose

d02prf resets the end point in an integration performed by d02pff and d02pgf.

2Specification

Fortran Interface
 Subroutine d02prf (
 Integer, Intent (Inout) :: iwsav(130), ifail Real (Kind=nag_wp), Intent (In) :: tendnu Real (Kind=nag_wp), Intent (Inout) :: rwsav(350)
#include <nag.h>
 void d02prf_ (const double *tendnu, Integer iwsav[], double rwsav[], Integer *ifail)
The routine may be called by the names d02prf or nagf_ode_ivp_rkts_reset_tend.

3Description

d02prf and its associated routines (d02pff, d02pgf, d02phf, d02pjf, d02pqf, d02psf, d02ptf and d02puf) solve the initial value problem for a first-order system of ordinary differential equations. The routines, based on Runge–Kutta methods and derived from RKSUITE (see Brankin et al. (1991)), integrate
 $y′=f(t,y) given y(t0)=y0$
where $y$ is the vector of $n$ solution components and $t$ is the independent variable.
d02prf is used to reset the final value of the independent variable, ${t}_{f}$, when the integration is already underway. It can be used to extend or reduce the range of integration. The new value must be beyond the current value of the independent variable (as returned in tnow by d02pff or d02pgf) in the current direction of integration. It is much more efficient to use d02prf for this purpose than to use d02pqf which involves the overhead of a complete restart of the integration.
If you want to change the direction of integration then you must restart by a call to d02pqf.

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: $\mathbf{tendnu}$Real (Kind=nag_wp) Input
On entry: the new value for ${t}_{f}$.
Constraint: $\mathrm{sign}\left({\mathbf{tendnu}}-{\mathbf{tnow}}\right)=\mathrm{sign}\left({\mathbf{tend}}-{\mathbf{tstart}}\right)$, where tstart and tend are as supplied in the previous call to d02pqf and tnow is returned by the preceding call to d02pff or d02pgf (i.e., integration must proceed in the same direction as before). tendnu must be distinguishable from tnow for the method and the machine precision being used.
2: $\mathbf{iwsav}\left(130\right)$Integer array Communication Array
3: $\mathbf{rwsav}\left(350\right)$Real (Kind=nag_wp) array Communication Array
Note: the communication array rwsav used by the other routines in the suite must be used here however, only the first $350$ elements will be referenced.
On entry: these must be the same arrays supplied in a previous call to d02pff or d02pgf. They must remain unchanged between calls.
On exit: information about the integration for use on subsequent calls to d02pff or d02pgf or other associated routines.
4: $\mathbf{ifail}$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, tendnu is not beyond tnow (step integrator) in the direction of integration.
The direction is negative, ${\mathbf{tendnu}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{tnow}}=⟨\mathit{\text{value}}⟩$.
On entry, tendnu is not beyond tnow (step integrator) in the direction of integration.
The direction is positive, ${\mathbf{tendnu}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{tnow}}=⟨\mathit{\text{value}}⟩$.
On entry, tendnu is too close to tnow (step integrator). Their difference is $⟨\mathit{\text{value}}⟩$, but this quantity must be at least $⟨\mathit{\text{value}}⟩$.
You cannot call this routine after the integrator has returned an error.
You cannot call this routine before you have called the setup routine.
You cannot call this routine before you have called the step integrator.
You cannot call this routine when the range integrator has been used.
${\mathbf{ifail}}=-99$
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.

Not applicable.

8Parallelism and Performance

d02prf is not threaded in any implementation.

None.

10Example

This example integrates a two body problem. The equations for the coordinates $\left(x\left(t\right),y\left(t\right)\right)$ of one body as functions of time $t$ in a suitable frame of reference are
 $x′′=-xr3$
 $y′′=-yr3, r=x2+y2.$
The initial conditions
 $x(0)=1-ε, x′(0)=0 y(0)=0, y′(0)= 1+ε 1-ε$
lead to elliptic motion with $0<\epsilon <1$. $\epsilon =0.7$ is selected and the system of ODEs is reposed as
 $y1′=y3 y2′=y4 y3′=- y1r3 y4′=- y2r3$
over the range $\left[0,6\pi \right]$. Relative error control is used with threshold values of $\text{1.0E−10}$ for each solution component and compute the solution at intervals of length $\pi$ across the range using d02prf to reset the end of the integration range. A high-order Runge–Kutta method (${\mathbf{method}}=-3$) is also used with tolerances ${\mathbf{tol}}=\text{1.0E−4}$ and ${\mathbf{tol}}=\text{1.0E−5}$ in turn so that the solutions may be compared.

10.1Program Text

Program Text (d02prfe.f90)

10.2Program Data

Program Data (d02prfe.d)

10.3Program Results

Program Results (d02prfe.r)