d02phc is a reverse communication function that computes the interpolant for evaluation by
d02pjc anywhere on an integration step taken by
d02pgc. The direct communication version of the
d02phc and
d02pjc pair is
d02psc. A significant difference in functionality between the forward and reverse communication versions is that
d02phc and
d02pjc can interpolate for the highorder Runge–Kutta method.
d02phc and its associated functions (
d02pgc,
d02pjc,
d02pqc,
d02prc,
d02ptc and
d02puc) solve the initial value problem for a firstorder system of ordinary differential equations. The functions, 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.
d02pgc computes the solution at the end of an integration step. Using the information computed on that step
d02phc computes the interpolant which can be evaluated at any point on that step by
d02pjc. If
${\mathbf{method}}=\mathrm{Nag\_RK\_2\_3}$ 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
${\mathbf{method}}=\mathrm{Nag\_RK\_4\_5}$ 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
${\mathbf{method}}=\mathrm{Nag\_RK\_7\_8}$ was specified in the call to setup function
d02pqc 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 function 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.
 NE_ALLOC_FAIL

Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
 NE_BAD_PARAM

On entry, argument $\u27e8\mathit{\text{value}}\u27e9$ had an illegal value.
 NE_INT

On entry, ${\mathbf{lwcomm}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: for ${\mathbf{method}}=\mathrm{Nag\_RK\_2\_3}$, ${\mathbf{lwcomm}}\ge 1$.
 NE_INT_2

On entry, ${\mathbf{lwcomm}}=\u27e8\mathit{\text{value}}\u27e9$ and ${\mathbf{nwant}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: for ${\mathbf{method}}=\mathrm{Nag\_RK\_7\_8}$, ${\mathbf{lwcomm}}\ge 8\times {\mathbf{nwant}}$.
On entry, ${\mathbf{nwant}}=\u27e8\mathit{\text{value}}\u27e9$ and ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$.
Constraint: $1\le {\mathbf{nwant}}\le {\mathbf{n}}$.
 NE_INT_3

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 ${\mathbf{method}}=\mathrm{Nag\_RK\_4\_5}$, ${\mathbf{lwcomm}}\ge {\mathbf{n}}+\mathrm{max}\phantom{\rule{0.125em}{0ex}}({\mathbf{n}},5\times {\mathbf{nwant}})$.
 NE_INT_CHANGED

On entry, ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$, but the value passed to the setup function was ${\mathbf{n}}=\u27e8\mathit{\text{value}}\u27e9$.
 NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
 NE_MISSING_CALL

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

Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
 NE_PREV_CALL_INI

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

You cannot call this function after the range integrator has been called.
The computed values will be of a similar accuracy to that computed by
d02pgc.
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 function. Please also consult the
Users' Note for your implementation for any additional implementationspecific information.
None.