naginterfaces.library.ode.ivp_​rkts_​diag

naginterfaces.library.ode.ivp_rkts_diag(comm)

ivp_rkts_diag provides details about an integration performed by either ivp_rkts_range(), ivp_rkts_onestep() or ivp_rk_step_revcomm().

For full information please refer to the NAG Library document for d02pt

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/d02/d02ptf.html

Parameters

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by prior calls to ivp_rkts_setup() and one of ivp_rkts_range(), ivp_rkts_onestep() or ivp_rk_step_revcomm().

Returns

fevalsint

The total number of evaluations of $f$ used in the integration so far; this includes evaluations of $f$ required for the secondary integration necessary if ivp_rkts_setup() had previously been called with $\text{method}>0$.

stepcostint

The cost in terms of number of evaluations of $f$ of a typical step with the method being used for the integration. The method is specified by the argument $\text{method}$ in a prior call to ivp_rkts_setup().

wastefloat

The number of attempted steps that failed to meet the local error requirement divided by the total number of steps attempted so far in the integration. A ‘large’ fraction indicates that the integrator is having trouble with the problem being solved. This can happen when the problem is ‘stiff’ and also when the solution has discontinuities in a low-order derivative.

stepsokint

The number of accepted steps.

hnextfloat

The step size the integrator will attempt to use for the next step.

Raises

NagValueError

(errno $1$)

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

(errno $1$)

You have already made one call to this function after the integrator could not achieve specified accuracy.

You cannot call this function again.

(errno $1$)

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.

Notes

ivp_rkts_diag and its associated functions (ivp_rkts_range(), ivp_rkts_onestep(), ivp_rk_step_revcomm(), ivp_rk_interp_setup(), ivp_rk_interp_eval(), ivp_rkts_setup(), ivp_rkts_reset_tend(), ivp_rkts_interp() and ivp_rkts_errass()) solve the initial value problem for a first-order system of ordinary differential equations. The functions, based on Runge–Kutta methods and derived from RKSUITE (see Brankin et al. (1991)), integrate

$$y^{\prime }=f(t,y)\text{given}y\left(t_0\right)=y_0$$

where $y$ is the vector of $n$ solution components and $t$ is the independent variable.

After a call to ivp_rkts_range(), ivp_rkts_onestep() or ivp_rk_step_revcomm(), ivp_rkts_diag can be called to obtain information about the cost of the integration and the size of the next step.

References

Brankin, R W, Gladwell, I and Shampine, L F, 1991, RKSUITE: A suite of Runge–Kutta codes for the initial value problems for ODEs, SoftReport 91-S1, Southern Methodist University