naginterfaces.library.ode.ivp_2nd_rkn_interp¶
- naginterfaces.library.ode.ivp_2nd_rkn_interp(t, y, yp, nwant, twant, comm)[source]¶
ivp_2nd_rkn_interp
interpolates components of the solution of a non-stiff system of second-order differential equations from information provided by the integratorivp_2nd_rkn()
, when the low-order method has been used.For full information please refer to the NAG Library document for d02lz
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/d02/d02lzf.html
- Parameters
- tfloat
, the current value at which the solution and its derivative have been computed (as returned in argument on output from
ivp_2nd_rkn()
).- yfloat, array-like, shape
The th component of the solution at , for , as returned from
ivp_2nd_rkn()
.- ypfloat, array-like, shape
The th component of the derivative at , for , as returned from
ivp_2nd_rkn()
.- nwantint
The number of components of the solution and derivative whose values at are required. The first components are evaluated.
- twantfloat
The point at which components of the solution and derivative are to be evaluated. should not normally be an extrapolation point, that is should satisfy
or if integration is proceeding in the negative direction
where told is the previous integration point which is held in an element of the array [‘rwork’] and is, to within rounding, . ( is given by
ivp_2nd_rkn_diag()
.) Extrapolation is permitted but not recommended, and = 2 is returned whenever extrapolation is attempted.- commdict, communication object, modified in place
Communication structure.
This argument must have been initialized by a prior call to
ivp_2nd_rkn_setup()
.
- Returns
- ywantfloat, ndarray, shape
The calculated value of the th component of the solution at , for .
- ypwantfloat, ndarray, shape
The calculated value of the th component of the derivative at , for .
- Raises
- NagValueError
- (errno )
On entry, , but in a previous call to the setup function .
- (errno )
The integrator function
ivp_2nd_rkn()
has not been called.- (errno )
No successful steps, interpolation impossible at .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, and .
Constraint: .
- (errno )
Interpolation is not permitted on data from the high order formulas.
- Warns
- NagAlgorithmicWarning
- (errno )
Extrapolation at .
- Notes
No equivalent traditional C interface for this routine exists in the NAG Library.
ivp_2nd_rkn_interp
evaluates the first () components of the solution of a non-stiff system of second-order ordinary differential equations at any point using a special Runge–Kutta–Nystrom formula (see Dormand and Prince (1986)) and information generated byivp_2nd_rkn()
when the low-order method has been used. This information must be presented unchanged toivp_2nd_rkn_interp
.ivp_2nd_rkn_interp
should not normally be used to extrapolate outside the range of the values fromivp_2nd_rkn()
.
- References
Dormand, J R and Prince, P J, 1986, Runge–Kutta–Nystrom triples, Mathematical Report TP-CS-86-05, Teesside Polytechnic