nag_pde_interp_1d_coll (d03pyc) (PDF version)
d03 Chapter Contents
d03 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_pde_interp_1d_coll (d03pyc)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_pde_interp_1d_coll (d03pyc) may be used in conjunction with either nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc). It computes the solution and its first derivative at user-specified points in the spatial coordinate.

2  Specification

#include <nag.h>
#include <nagd03.h>
void  nag_pde_interp_1d_coll (Integer npde, const double u[], Integer nbkpts, const double xbkpts[], Integer npoly, Integer npts, const double xp[], Integer intpts, Integer itype, double up[], double rsave[], Integer lrsave, NagError *fail)

3  Description

nag_pde_interp_1d_coll (d03pyc) is an interpolation function for evaluating the solution of a system of partial differential equations (PDEs), or the PDE components of a system of PDEs with coupled ordinary differential equations (ODEs), at a set of user-specified points. The solution of a system of equations can be computed using nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc) on a set of mesh points; nag_pde_interp_1d_coll (d03pyc) can then be employed to compute the solution at a set of points other than those originally used in nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc). It can also evaluate the first derivative of the solution. Polynomial interpolation is used between each of the break points xbkpts[i-1], for i=1,2,,nbkpts. When the derivative is needed (itype=2), the array xp[intpts-1] must not contain any of the break points, as the method, and consequently the interpolation scheme, assumes that only the solution is continuous at these points.

4  References


5  Arguments

Note: the arguments u, npts, npde, xbkpts, nbkpts, rsave and lrsave must be supplied unchanged from either nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).
1:     npdeIntegerInput
On entry: the number of PDEs.
Constraint: npde1.
2:     u[npde×npts]const doubleInput
On entry: the PDE part of the original solution returned in the argument u by the function nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).
3:     nbkptsIntegerInput
On entry: the number of break points.
Constraint: nbkpts2.
4:     xbkpts[nbkpts]const doubleInput
On entry: xbkpts[i-1], for i=1,2,,nbkpts, must contain the break points as used by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).
Constraint: xbkpts[0]<xbkpts[1]<<xbkpts[nbkpts-1].
5:     npolyIntegerInput
On entry: the degree of the Chebyshev polynomial used for approximation as used by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).
Constraint: 1npoly49.
6:     nptsIntegerInput
On entry: the number of mesh points as used by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).
Constraint: npts=nbkpts-1×npoly+1.
7:     xp[intpts]const doubleInput
On entry: xp[i-1], for i=1,2,,intpts, must contain the spatial interpolation points.
  • xbkpts[0]xp[0]<xp[1]<<xp[intpts-1]xbkpts[nbkpts-1];
  • if itype=2, xp[i-1]xbkpts[j-1], for i=1,2,,intpts and j=2,3,,nbkpts-1.
8:     intptsIntegerInput
On entry: the number of interpolation points.
Constraint: intpts1.
9:     itypeIntegerInput
On entry: specifies the interpolation to be performed.
The solution at the interpolation points are computed.
Both the solution and the first derivative at the interpolation points are computed.
Constraint: itype=1 or 2.
10:   up[npde×intpts×itype]doubleOutput
Note: the element UPi,j,k is stored in the array element up[k-1×npde×intpts+j-1×intpts+i-1].
On exit: if itype=1, UPi,j,1, contains the value of the solution Uixj,tout, at the interpolation points xj=xp[j-1], for j=1,2,,intpts and i=1,2,,npde.
If itype=2, UPi,j,1 contains Uixj,tout and UPi,j,2 contains Ui x  at these points.
11:   rsave[lrsave]doubleCommunication Array
The array rsave contains information required by nag_pde_interp_1d_coll (d03pyc) as returned by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc). The contents of rsave must not be changed from the call to nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc). Some elements of this array are overwritten on exit.
12:   lrsaveIntegerInput
On entry: the size of the workspace rsave, as in nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
Extrapolation is not allowed.
On entry, itype=2 and at least one interpolation point coincides with a break point, i.e., interpolation point no value with value value is close to break point value with value value.
On entry, intpts0: intpts=value.
On entry, itype=value.
Constraint: itype=1 or 2.
On entry, nbkpts=value.
Constraint: nbkpts2.
On entry, npde=value.
Constraint: npde>0.
On entry, npoly=value.
Constraint: npoly>0.
On entry, npts=value, nbkpts=value and npoly=value.
Constraint: npts=nbkpts-1×npoly+1.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
On entry, break points xbkpts badly ordered: i=value, xbkpts[i-1]=value, j=value and xbkpts[j-1]=value.
On entry, interpolation points xp badly ordered: i=value, xp[i-1]=value, j=value and xp[j-1]=value.

7  Accuracy

See the documents for nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).

8  Further Comments


9  Example

See Section 9 in nag_pde_parab_1d_coll (d03pdc).

nag_pde_interp_1d_coll (d03pyc) (PDF version)
d03 Chapter Contents
d03 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012