NAG Library Function Document

nag_ode_ivp_rk_interp_eval (d02pjc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{icheck}$ – Nag_BooleanInput

On entry: indicates whether consistency checks on input arguments should be performed

$\mathbf{icheck}=\mathrm{Nag\_FALSE}$

Don't perform checks on input arguments.

$\mathbf{icheck}=\mathrm{Nag\_TRUE}$

Perform consistency checks on input arguments.

It is recommended to use $\mathbf{icheck}=\mathrm{Nag\_TRUE}$ on the first call following a call to nag_ode_ivp_rk_interp_setup (d02phc) and to set $\mathbf{icheck}=\mathrm{Nag\_FALSE}$ on subsequent calls within the last step to avoid the overhead of argument checking.

2:    $\mathbf{n}$ – IntegerInput

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 nag_ode_ivp_rkts_setup (d02pqc).

3:    $\mathbf{nwant}$ – IntegerInput

On entry: only the first nwant system components to be computed. This should be the same value as passed to nag_ode_ivp_rk_interp_setup (d02phc) when computing the interpolant.

Constraint: $\mathbf{nwant}=\mathbf{nwant}$ passed to nag_ode_ivp_rk_interp_setup (d02phc).

4:    $\mathbf{t}$ – doubleInput

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 nag_ode_ivp_rk_step_revcomm (d02pgc).

5:    $\mathbf{ideriv}$ – IntegerInput

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:    $\mathbf{sol}\left[\mathbf{nwant}\right]$ – doubleOutput

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:    $\mathbf{wcomm}\left[\mathbf{lwcomm}\right]$ – doubleCommunication Array

On entry: this must be the same array supplied in a previous call to nag_ode_ivp_rk_interp_setup (d02phc). It must remain unchanged between calls.

8:    $\mathbf{lwcomm}$ – IntegerInput

On entry: length of wcomm. This should be the same value as supplied in a previous call to nag_ode_ivp_rk_interp_setup (d02phc).

If in a previous call to nag_ode_ivp_rkts_setup (d02pqc):

• $\mathbf{method}=\mathrm{Nag\_RK\_2\_3}$, lwcomm must be at least $1$.
• $\mathbf{method}=\mathrm{Nag\_RK\_4\_5}$, lwcomm must be at least $\mathbf{n}+\max \left(\mathbf{n},5\times \mathbf{nwant}\right)$.
• $\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$, $\mathbf{lwcomm}\ge 8\times \mathbf{nwant}$.

9:    $\mathbf{iwsav}\left[130\right]$ – IntegerCommunication Array

10:  $\mathbf{rwsav}\left[32\times \mathbf{n}+350\right]$ – doubleCommunication Array

On entry: these must be the same arrays supplied in a previous call nag_ode_ivp_rk_step_revcomm (d02pgc). They must remain unchanged between calls.

On exit: information about the integration for use on subsequent calls to nag_ode_ivp_rk_step_revcomm (d02pgc), nag_ode_ivp_rk_interp_setup (d02phc) or other associated functions.

11:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{ideriv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ideriv}=0$ or $1$.

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

NE_INT_2

On entry, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$ and $\mathbf{nwant}=〈\mathit{\text{value}}〉$.
Constraint: for $\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$, $\mathbf{lwcomm}\ge 8\times \mathbf{nwant}$.

NE_INT_3

On entry, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{nwant}=〈\mathit{\text{value}}〉$.
Constraint: for $\mathbf{method}=\mathrm{Nag\_RK\_4\_5}$, $\mathbf{lwcomm}\ge \mathbf{n}+\max \left(\mathbf{n},5\times \mathbf{nwant}\right)$.

NE_INT_CHANGED

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.

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation 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 interpolation setup.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_PREV_CALL_INI

The previous call to the interpolation setup function returned an error.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example