NAG Library Function Document

nag_ode_ivp_rkts_interp (d02psc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 1$.

2:    $\mathbf{twant}$ – doubleInput

On entry: $t$, the value of the independent variable where a solution is desired.

3:    $\mathbf{reqest}$ – Nag_SolDerivInput

On entry: determines whether the solution and/or its first derivative are to be computed

$\mathbf{reqest}=\mathrm{Nag\_Sol}$

compute approximate solution.

$\mathbf{reqest}=\mathrm{Nag\_Der}$

compute approximate first derivative.

$\mathbf{reqest}=\mathrm{Nag\_SolDer}$

compute approximate solution and first derivative.

Constraint: $\mathbf{reqest}=\mathrm{Nag\_Sol}$, $\mathrm{Nag\_Der}$ or $\mathrm{Nag\_SolDer}$.

4:    $\mathbf{nwant}$ – IntegerInput

On entry: the number of components of the solution to be computed. The first nwant components are evaluated.

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

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

On exit: an approximation to the first nwant components of the solution at twant if $\mathbf{reqest}=\mathrm{Nag\_Sol}$ or $\mathrm{Nag\_SolDer}$. Otherwise ywant is not defined.

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

On exit: an approximation to the first nwant components of the first derivative at twant if $\mathbf{reqest}=\mathrm{Nag\_Der}$ or $\mathrm{Nag\_SolDer}$. Otherwise ypwant is not defined.

7:    $\mathbf{f}$ – function, supplied by the userExternal Function

f must evaluate the functions $f_i$ (that is the first derivatives $y_i^{\prime }$) for given values of the arguments $t,y_i$. It must be the same procedure as supplied to nag_ode_ivp_rkts_onestep (d02pfc).

The specification of f is:

void  f (double t, Integer n, const double y[], double yp[], Nag_Comm *comm)

1:    $\mathbf{t}$ – doubleInput

On entry: $t$, the current value of the independent variable.

2:    $\mathbf{n}$ – IntegerInput

On entry: $\mathit{n}$, the number of ordinary differential equations in the system to be solved.

3:    $\mathbf{y}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the current values of the dependent variables, $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,\mathit{n}$.

4:    $\mathbf{yp}\left[\mathbf{n}\right]$ – doubleOutput

On exit: the values of $f_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,\mathit{n}$.

5:    $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to f.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_ode_ivp_rkts_interp (d02psc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_ode_ivp_rkts_interp (d02psc) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_ode_ivp_rkts_interp (d02psc). If your code inadvertently does return any NaNs or infinities, nag_ode_ivp_rkts_interp (d02psc) is likely to produce unexpected results.

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

On entry: this array stores information that can be utilized on subsequent calls to nag_ode_ivp_rkts_interp (d02psc).

9:    $\mathbf{lwcomm}$ – IntegerInput

On entry: length of wcomm.

If in a previous call to nag_ode_ivp_rkts_setup (d02pqc):

• $\mathbf{method}=\mathrm{Nag\_RK\_2\_3}$ then lwcomm must be at least $1$.
• $\mathbf{method}=\mathrm{Nag\_RK\_4\_5}$ then lwcomm must be at least $\mathbf{n}+\max \left(\mathbf{n},5\times \mathbf{nwant}\right)$.
• $\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$ then wcomm and lwcomm are not referenced.

10:  $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

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

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

On entry: these must be the same arrays supplied in a previous call nag_ode_ivp_rkts_onestep (d02pfc). They must remain unchanged between calls.

On exit: information about the integration for use on subsequent calls to nag_ode_ivp_rkts_onestep (d02pfc), nag_ode_ivp_rkts_interp (d02psc) or other associated functions.

13:  $\mathbf{fail}$ – 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, $\mathbf{nwant}=〈\mathit{\text{value}}〉$ 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

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

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.

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 when you have specified, in the setup function, that the range integrator will be used.

NE_RK_NO_INTERP

$\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$ in setup, but interpolation is not available for this method. Either use $\mathbf{method}=\mathrm{Nag\_RK\_4\_5}$ in setup or use reset function to force the integrator to step to particular points.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d02psce.c)

10.2

Program Data

Program Data (d02psce.d)

10.3

Program Results

Program Results (d02psce.r)