NAG Library Function Document

nag_ode_ivp_rk_interp_setup (d02phc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{irevcm}$ – Integer *Input/Output

On initial entry: irevcm must be set to zero to indicate that the interpolant for a new step is being taken.

On intermediate re-entry: irevcm should remain unchanged.

On intermediate exit: irevcm returns a value $1$ to indicate that a function evaluation is required prior to re-entry; the value of the derivatives must be returned in yp where the value of $t$ is supplied in t and the values $y\left(t\right)$ are supplied in the array y.

On final exit:

$\mathbf{irevcm}=-1$

Successful exit; rwsav and wcomm contain details of the interpolant.

$\mathbf{irevcm}=-2$

Error exit; fail should be interrogated to determine the nature of the error.

Note: any values you return to nag_ode_ivp_rk_interp_setup (d02phc) as part of the reverse communication procedure should not include floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_ode_ivp_rk_interp_setup (d02phc). If your code inadvertently does return any NaNs or infinities, nag_ode_ivp_rk_interp_setup (d02phc) is likely to produce unexpected results.

2:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of ordinary differential equations in the system to be solved by the integration function.

Constraint: $\mathbf{n}\ge 1$. 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: the number of components of the solution to be computed. The first nwant components are evaluated.

Constraint: $1\le \mathbf{nwant}\le \mathbf{n}$.

4:    $\mathbf{t}$ – double *Output

On intermediate exit: t contains the value of the independent variable $t$ at which the derivatives $y^{\prime }$ are to be evaluated.

On final exit: contains no useful information.

5:    $\mathbf{y}\left[\mathbf{n}\right]$ – doubleOutput

On intermediate exit: y contains the value of the solution $y$ at which the derivatives $y^{\prime }$ are to be evaluated.

On final exit: contains no useful information.

6:    $\mathbf{yp}\left[\mathbf{n}\right]$ – const doubleInput

On initial entry: need not be set.

On intermediate re-entry: yp must contain the values of the derivatives $y_i^{\prime }$ for the given values of the parameters $t$, $y_i$.

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

On entry: wcomm need not be set.

On intermediate re-entry: wcomm contains the partial computation of the polynomial coefficients corresponding to a continuous Runge–Kutta process for interpolating medium and high order Runge–Kutta methods.

On final exit: if $\mathbf{method}=\mathrm{Nag\_RK\_4\_5}$ or $\mathrm{Nag\_RK\_7\_8}$, wcomm contains details of the interpolant which must be passed unchanged to nag_ode_ivp_rk_interp_eval (d02pjc) for evaluation of the interpolant.

8:    $\mathbf{lwcomm}$ – IntegerInput

On entry: length of wcomm.

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

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_eval (d02pjc) or other associated functions.

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

The NAG error argument (see Section 3.7 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, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$.
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 $\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$, $\mathbf{lwcomm}\ge 8\times \mathbf{nwant}$.

On entry, $\mathbf{nwant}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{nwant}\le \mathbf{n}$.

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 function was $\mathbf{n}=〈\mathit{\text{value}}〉$.

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 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 step integrator.

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

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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

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Example