naginterfaces.library.ode.ivp_​2nd_​rkn_​setup

naginterfaces.library.ode.ivp_2nd_rkn_setup(h, tol, thres, thresp, maxstp, start, onestp, high, comm)

ivp_2nd_rkn_setup is a setup function which must be called prior to the first call of the integrator ivp_2nd_rkn() and may be called prior to any continuation call to ivp_2nd_rkn().

For full information please refer to the NAG Library document for d02lx

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d02/d02lxf.html

Parameters

hfloat

If $start=True$, $h$ may specify an initial step size to be attempted in ivp_2nd_rkn().

If $start=False$, $h$ may specify a step size to override the choice of next step attempted made internally to ivp_2nd_rkn().

The sign of $h$ is not important, as the absolute value of $h$ is chosen and the appropriate sign is selected by ivp_2nd_rkn().

If this option is not required then you must set $h=0.0$.

tolfloat

Must be set to a relative tolerance for controlling the error in the integration by ivp_2nd_rkn(). ivp_2nd_rkn() has been designed so that, for most problems, a reduction in $tol$ leads to an approximately proportional reduction in the error in the solution. However the actual relation between $tol$ and the accuracy of the solution cannot be guaranteed. You are strongly recommended to repeat the integration with a smaller value of $tol$ and compare the results. See the description of $thres$ and $thresp$ for further details of how $tol$ is used.

thresfloat, array-like, shape $\left(\text{neq}\right)$

$thres$ and $thresp$ may be set to thresholds for use in the error control of ivp_2nd_rkn(). At each step in the numerical integration estimates of the local errors $E1\left(\text{i}\right)$ and $E2\left(\text{i}\right)$ in the solution, $y_{\text{i}}$, and its derivative, $y_{\text{i}}^{\prime }$, respectively are computed, for $\text{i}=1,2,\dots ,\text{neq}$. For the step to be accepted conditions of the following type must be satisfied:

$$\begin{array}{c}\begin{array}{c}{max}_{1\le i\le \text{neq}}\left(\frac{E1\left(i\right)}{max\left(thres\right[i-1],\left|y_i\right|)}\right)\le tol\text{,}\\ \\ \\ {max}_{1\le i\le \text{neq}}\left(\frac{E2\left(i\right)}{max\left(thresp\right[i-1],\left|y_i^{\prime }\right|)}\right)\le tol\text{.}\end{array}\end{array}$$

If one or both of these is not satisfied then the step size is reduced and the solution is recomputed.

If $thres\left[0\right]\le 0.0$ on entry, a value of $50.0\times ϵ$ is used for $thres[\text{i}-1]$, for $\text{i}=1,2,\dots ,\text{neq}$, where $ϵ$ is machine precision.

Similarly for $thresp$.

threspfloat, array-like, shape $\left(\text{neq}\right)$

$thresp$ and $thresp$ may be set to thresholds for use in the error control of ivp_2nd_rkn(). At each step in the numerical integration estimates of the local errors $E1\left(\text{i}\right)$ and $E2\left(\text{i}\right)$ in the solution, $y_{\text{i}}$, and its derivative, $y_{\text{i}}^{\prime }$, respectively are computed, for $\text{i}=1,2,\dots ,\text{neq}$. For the step to be accepted conditions of the following type must be satisfied:

$$\begin{array}{c}\begin{array}{c}{max}_{1\le i\le \text{neq}}\left(\frac{E1\left(i\right)}{max\left(thres\right[i-1],\left|y_i\right|)}\right)\le tol\text{,}\\ \\ \\ {max}_{1\le i\le \text{neq}}\left(\frac{E2\left(i\right)}{max\left(thresp\right[i-1],\left|y_i^{\prime }\right|)}\right)\le tol\text{.}\end{array}\end{array}$$

If one or both of these is not satisfied then the step size is reduced and the solution is recomputed.

If $thres\left[0\right]\le 0.0$ on entry, a value of $50.0\times ϵ$ is used for $thres[\text{i}-1]$, for $\text{i}=1,2,\dots ,\text{neq}$, where $ϵ$ is machine precision.

Similarly for $thresp$.

maxstpint

A bound on the number of steps attempted in any one call of ivp_2nd_rkn().

If $maxstp\le 0$ on entry, a value of $1000$ is used.

startbool

Specifies whether or not the call of ivp_2nd_rkn() is for a new problem. $start=True$ indicates that a new problem is to be solved. $start=False$ indicates the call of ivp_2nd_rkn_setup is prior to a continuation call of ivp_2nd_rkn().

onestpbool

The mode of operation for ivp_2nd_rkn().

$onestp=True$

ivp_2nd_rkn() will operate in one-step mode, that is it will return after each successful step.

$onestp=False$

ivp_2nd_rkn() will operate in interval mode, that is it will return at the end of the integration interval.

highbool

If $high=True$, a high-order method will be used, whereas if $high=False$, a low-order method will be used. (See the specification of ivp_2nd_rkn() for further details.)

commdict, communication object, modified in place

Communication structure.

On initial entry: need not be set.

Returns

startbool

$start=False$.

Raises

NagValueError

(errno $1$)

On entry, $thresp[⟨value⟩]=⟨value⟩$ is not positive.

(errno $1$)

On entry, $thres[⟨value⟩]=⟨value⟩$ is not positive.

(errno $2$)

On entry, $\text{neq}=⟨value⟩$.

Constraint: $\text{neq}\ge 1$.

(errno $2$)

On entry, $high=False$ and $\text{lrwork}=⟨value⟩$.

Constraint: if $high=False$ then $\text{lrwork}\ge ⟨value⟩$.

(errno $2$)

On entry, $high=True$ and $\text{lrwork}=⟨value⟩$.

Constraint: if $high=True$ then $\text{lrwork}\ge ⟨value⟩$.

(errno $3$)

On entry, $tol=⟨value⟩$.

Constraint: $⟨value⟩<tol<⟨value⟩$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

ivp_2nd_rkn_setup permits you to set optional inputs prior to any call of ivp_2nd_rkn(). It must be called before the first call of function ivp_2nd_rkn() and it may be called before any continuation call of function ivp_2nd_rkn().