where is the vector of solution components and is the independent variable.
After a call to d02pef,d02pfford02pgf, d02ptf can be called to obtain information about the cost of the integration and the size of the next step.
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
1: – IntegerOutput
On exit: the total number of evaluations of used in the integration so far; this includes evaluations of required for the secondary integration necessary if d02pqf had previously been called with .
2: – IntegerOutput
On exit: the cost in terms of number of evaluations of of a typical step with the method being used for the integration. The method is specified by the argument method in a prior call to d02pqf.
3: – Real (Kind=nag_wp)Output
On exit: 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.
4: – IntegerOutput
On exit: the number of accepted steps.
5: – Real (Kind=nag_wp)Output
On exit: the step size the integrator will attempt to use for the next step.
6: – Integer arrayCommunication Array
7: – Real (Kind=nag_wp) arrayCommunication Array
Note: the communication rwsav used by the other routines in the suite must be used here however, only the first elements will be referenced.
On entry: these must be the same arrays supplied in a previous call to d02pef,d02pfford02pgf. They must remain unchanged between calls.
On exit: information about the integration for use on subsequent calls to d02pef,d02pfford02pgf or other associated routines.
8: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, a previous call to the setup routine 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.
You cannot call this routine before you have called the integrator.
You have already made one call to this routine after the integrator could not achieve specified accuracy. You cannot call this routine again.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
d02ptf is not threaded in any implementation.
When a secondary integration has taken place, that is when global error assessment has been specified using
in a prior call to d02pqf, then the approximate number of evaluations of used in this secondary integration is given by for or and for .