NAG Library Function Document

nag_ode_ivp_rkts_onestep (d02pfc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{f}$ – 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 $t$, $y_i$.

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_onestep (d02pfc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_ode_ivp_rkts_onestep (d02pfc) (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_onestep (d02pfc). If your code inadvertently does return any NaNs or infinities, nag_ode_ivp_rkts_onestep (d02pfc) 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.

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

3:    $\mathbf{tnow}$ – double *Output

On exit: $t$, the value of the independent variable at which a solution has been computed.

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

On exit: an approximation to the solution at tnow. The local error of the step to tnow was no greater than permitted by the specified tolerances (see nag_ode_ivp_rkts_setup (d02pqc)).

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

On exit: an approximation to the first derivative of the solution at tnow.

6:    $\mathbf{comm}$ – Nag_Comm *

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

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

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

On entry: these must be the same arrays supplied in a previous call to nag_ode_ivp_rkts_setup (d02pqc). They must remain unchanged between calls.

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

9:    $\mathbf{fail}$ – 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_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.

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, 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

A call to this function cannot be made after it has returned an error.
The setup function must be called to start another problem.

NE_RK_GLOBAL_ERROR_S

The global error assessment algorithm failed at start of integration.
The integration is being terminated.

NE_RK_GLOBAL_ERROR_T

The global error assessment may not be reliable for times beyond $〈\mathit{\text{value}}〉$.
The integration is being terminated.

NE_RK_POINTS

More than $100$ output points have been obtained by integrating to tend (as specified in the setup function). They have been so clustered that it would probably be (much) more efficient to use the interpolation function (if $\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$, switch to $\mathbf{method}=\mathrm{Nag\_RK\_4\_5}$ at setup). However, you can continue integrating the problem.

NE_RK_STEP_TOO_SMALL

In order to satisfy your error requirements the solver has to use a step size of $〈\mathit{\text{value}}〉$ at the current time, $〈\mathit{\text{value}}〉$. This step size is too small for the machine precision, and is smaller than $〈\mathit{\text{value}}〉$.

NE_RK_TGOT_EQ_TEND

tend, as specified in the setup function, has already been reached. To start a new problem, you will need to call the setup function. To continue integration beyond tend then nag_ode_ivp_rkts_reset_tend (d02prc) must first be called to reset tend to a new end value.

NE_STIFF_PROBLEM

Approximately $〈\mathit{\text{value}}〉$ function evaluations have been used to compute the solution since the integration started or since this message was last printed. Your problem has been diagnosed as stiff. If the situation persists, it will cost roughly $〈\mathit{\text{value}}〉$ times as much to reach tend (setup) as it has cost to reach the current time. You should probably call functions intended for stiff problems. However, you can continue integrating the problem.

NW_RK_TOO_MANY

Approximately $〈\mathit{\text{value}}〉$ function evaluations have been used to compute the solution since the integration started or since this message was last printed. However, you can continue integrating the problem.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d02pfce.c)

10.2

Program Data

Program Data (d02pfce.d)

10.3

Program Results

Program Results (d02pfce.r)