NAG FL Interface
d02nwf (ivp_​stiff_​blend)

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1 Purpose

d02nwf is a setup routine which must be called prior to linear algebra setup routines and integrators from the SPRINT suite of routines, if the BLEND formulae are to be used.

2 Specification

Fortran Interface
Subroutine d02nwf ( neqmax, sdysav, maxord, con, tcrit, hmin, hmax, h0, maxstp, mxhnil, norm, rwork, ifail)
Integer, Intent (In) :: neqmax, sdysav, maxord, maxstp, mxhnil
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: tcrit, hmin, hmax, h0
Real (Kind=nag_wp), Intent (Inout) :: con(6), rwork(50+4*neqmax)
Character (1), Intent (In) :: norm
C Header Interface
#include <nag.h>
void  d02nwf_ (const Integer *neqmax, const Integer *sdysav, const Integer *maxord, double con[], const double *tcrit, const double *hmin, const double *hmax, const double *h0, const Integer *maxstp, const Integer *mxhnil, const char *norm, double rwork[], Integer *ifail, const Charlen length_norm)
The routine may be called by the names d02nwf or nagf_ode_ivp_stiff_blend.

3 Description

An integrator setup routine must be called before the call to any linear algebra setup routine or integrator from the SPRINT suite of routines in this sub-chapter. This setup routine, d02nwf, makes the choice of the BLEND integrator and permits you to define options appropriate to this choice. Alternative choices of integrator from this suite are the BDF method and the DASSL implementation of the BDF method which can be chosen by initial calls to d02nvf or d02mvf respectively.

4 References

See the D02M–N Sub-chapter Introduction.

5 Arguments

1: neqmax Integer Input
On entry: a bound on the maximum number of differential equations to be solved.
Constraint: neqmax1.
2: sdysav Integer Input
On entry: the second dimension of the array ysav that will be supplied to the integrator, as declared in the (sub)program from which the integrator is called (e.g., see d02nbf).
Constraint: sdysavmaxord+3.
3: maxord Integer Input
On entry: the maximum order to be used for the BLEND method.
Constraint: 0<maxord11.
4: con(6) Real (Kind=nag_wp) array Input/Output
On entry: values to be used to control step size choice during integration. If any con(i)=0.0 on entry, it is replaced by its default value described below. In most cases this is the recommended setting.
con(1), con(2), and con(3) are factors used to bound step size changes. If the current step size h fails, the modulus of the next step size is bounded by con(1)×|h|. The default value of con(1) is 2.0. Note that the new step size may be used with a method of different order to the failed step. If the initial step size is h, the modulus of the step size on the second step is bounded by con(3)×|h|. At any other stage in the integration, if the current step size is h, the modulus of the next step size is bounded by con(2)×|h|. The default values are 10.0 for con(2) and 1000.0 for con(3).
con(4), con(5) and con(6) are ‘tuning’ constants used in determining the next order and step size. They are used to scale the error estimates used in determining whether to keep the same order of the BLEND method, decrease the order or increase the order respectively. The larger the value of con(i), for i=4,5,6, the less likely the choice of the corresponding order. The default values are: con(4)=1.2, con(5)=1.3, con(6)=1.4.
These constraints must be satisfied after any zero values have been replaced by their default values.
  • 0.0<con(1)con(2)con(3);
  • con(i)1.0, for i=2,3,,6.
On exit: the values actually used by d02nwf.
5: tcrit Real (Kind=nag_wp) Input
On entry: a point beyond which integration must not be attempted. The use of tcrit is described under the argument itask in the specification for the integrator (e.g., see d02nbf). A value, 0.0 say, must be specified even if itask subsequently specifies that tcrit will not be used.
6: hmin Real (Kind=nag_wp) Input
On entry: the minimum absolute step size to be allowed. Set hmin=0.0 if this option is not required.
7: hmax Real (Kind=nag_wp) Input
On entry: the maximum absolute step size to be allowed. Set hmax=0.0 if this option is not required.
8: h0 Real (Kind=nag_wp) Input
On entry: the step size to be attempted on the first step. Set h0=0.0 if the initial step size is calculated internally.
9: maxstp Integer Input
On entry: the maximum number of steps to be attempted during one call to the integrator after which it will return with ifail=2. Set maxstp=0 if no limit is to be imposed.
10: mxhnil Integer Input
On entry: the maximum number of warnings printed (if itrace0, e.g., see d02nbf) per problem when t+h=t on a step (h=​ current step size). If mxhnil0, a default value of 10 is assumed.
11: norm Character(1) Input
On entry: indicates the type of norm to be used.
Maximum norm.
Averaged L2 norm.
Is the same as 'A'.
If vnorm denotes the norm of the vector v of length n, for the averaged L2 norm
while for the maximum norm
If you wish to weight the maximum norm or the L2 norm, rtol and atol should be scaled appropriately on input to the integrator (see under itol in the specification of the integrator for the formulation of the weight vector wi from rtol and atol, e.g., d02nbf).
Only the first character of the actual argument norm is passed to d02nwf; hence it is permissible for the actual argument to be more descriptive e.g., ‘Maximum’, ‘Average L2’ or ‘Default’ in a call to d02nwf.
Constraint: norm='M', 'A' or 'D'.
12: rwork(50+4×neqmax) Real (Kind=nag_wp) array Communication Array
This must be the same workspace array as the array rwork supplied to the integrator. It is used to pass information from the setup routine to the integrator and, therefore, the contents of this array must not be changed before calling the integrator.
13: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, con(value)=value was less than 0.0.
On entry, con(value)=value was less than 1.0.
On entry, con(1)=value and con(2)=value.
Constraint: con(1)con(2).
On entry, con(2)=value and con(3)=value.
Constraint: con(2)con(3).
On entry, maxord=value.
Constraint: 0<maxord11.
On entry, maxord=value and sdysav=value.
Constraint: sdysavmaxord+3.
On entry, neqmax=value.
Constraint: neqmax1.
On entry, norm=value.
Constraint: norm='M', 'A' or 'D'.
An unexpected error has been triggered by this routine. Please contact NAG.
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
d02nwf is not threaded in any implementation.

9 Further Comments


10 Example

See d02ncf.