NAG Library Function Document

nag_ode_ivp_rkts_interp (d02psc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     twant – doubleInput

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

3:     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:     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:     ywant[nwant] – 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:     ypwant[nwant] – 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:     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:     t – doubleInput

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

2:     n – IntegerInput

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

3:     y[n] – const doubleInput

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

4:     yp[n] – doubleOutput

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

5:     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 3.2.1.1 in the Essential Introduction).

8:     wcomm[lwcomm] – doubleCommunication Array

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

9:     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:   comm – Nag_Comm *Communication Structure

The NAG communication argument (see Section 3.2.1.1 in the Essential Introduction).

11:   iwsav[$130$] – IntegerCommunication Array

12:   rwsav[$32\times \mathbf{n}+350$] – 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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.

NE_MISSING_CALL

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

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)