d02phf is a reverse communication routine that computes the interpolant for evaluation by
d02pjf anywhere on an integration step taken by
d02pgf. The direct communication version of the
d02phf and
d02pjf pair is
d02psf. A significant difference in functionality between the forward and reverse communication versions is that
d02phf and
d02pjf can interpolate for the highorder Runge–Kutta method.
d02phf and its associated routines (
d02pgf,
d02pjf,
d02pqf,
d02prf,
d02ptf and
d02puf) solve the initial value problem for a firstorder system of ordinary differential equations. The routines, based on Runge–Kutta methods and derived from RKSUITE (see
Brankin et al. (1991)), integrate
where
$y$ is the vector of
$\mathit{n}$ solution components and
$t$ is the independent variable.
d02pgf computes the solution at the end of an integration step. Using the information computed on that step
d02phf computes the interpolant which can be evaluated at any point on that step by
d02pjf. If
${\mathbf{method}}=1$ or
$\mathrm{1}$ 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
${\mathbf{method}}=2$ or
$\mathrm{2}$ 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
${\mathbf{method}}=3$ or
$\mathrm{3}$ was specified in the call to setup routine
d02pqf then the interpolant is a continuous Runge–Kutta process requiring a further
$7$ stages of derivative evaluations that will be requested in turn.
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 91S1 Southern Methodist University
Note: this routine uses
reverse communication. Its use involves an initial entry, intermediate exits and reentries, and a final exit, as indicated by the argument
irevcm. Between intermediate exits and reentries,
all arguments other than those specified by the value of irevcm must remain unchanged.
If on entry
${\mathbf{ifail}}=0$ or
$\mathrm{1}$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
 ${\mathbf{ifail}}=1$

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, ${\mathbf{lwcomm}}=\u27e8\mathit{\text{value}}\u27e9$, ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$ and ${\mathbf{nwant}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: for ${\mathbf{method}}=\mathrm{2}$ or $2$, ${\mathbf{lwcomm}}\ge {\mathbf{n}}+\mathrm{max}\phantom{\rule{0.125em}{0ex}}({\mathbf{n}},5\times {\mathbf{nwant}})$.
On entry, ${\mathbf{lwcomm}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: for ${\mathbf{method}}=\mathrm{1}$ or $1$, ${\mathbf{lwcomm}}\ge 1$.
On entry, ${\mathbf{lwcomm}}=\u27e8\mathit{\text{value}}\u27e9$ and ${\mathbf{nwant}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: for ${\mathbf{method}}=\mathrm{3}$ or $3$, ${\mathbf{lwcomm}}\ge 8\times {\mathbf{nwant}}$.
On entry, ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$, but the value passed to the setup routine was ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$.
On entry, ${\mathbf{nwant}}=\u27e8\mathit{\text{value}}\u27e9$ and ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: $1\le {\mathbf{nwant}}\le {\mathbf{n}}$.
You cannot call this routine after the integrator has returned an error.
You cannot call this routine after the range integrator has been called.
You cannot call this routine before you have called the step integrator.
The computed values will be of a similar accuracy to that computed by
d02pgf.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementationspecific information.
None.