NAG Library Routine Document

D03PZF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NPDE – INTEGERInput

On entry: the number of PDEs.

Constraint: $\mathbf{NPDE}\ge 1$.

2:     M – INTEGERInput

On entry: the coordinate system used. If the call to D03PZF follows one of the finite difference routines then M must be the same parameter M as used in that call. For the Keller box scheme only Cartesian coordinate systems are valid and so M must be set to zero. No check will be made by D03PZF in this case.

$\mathbf{M}=0$

Indicates Cartesian coordinates.

$\mathbf{M}=1$

Indicates cylindrical polar coordinates.

$\mathbf{M}=2$

Indicates spherical polar coordinates.

Constraints:

• $0\le \mathbf{M}\le 2$ following a finite difference routine;
• $\mathbf{M}=0$ following a Keller box scheme routine.

3:     U(NPDE,NPTS) – REAL (KIND=nag_wp) arrayInput

On entry: the PDE part of the original solution returned in the parameter U by the PDE routine.

Constraint: $\mathbf{NPDE}\ge 1$.

4:     NPTS – INTEGERInput

On entry: the number of mesh points.

Constraint: $\mathbf{NPTS}\ge 3$.

5:     X(NPTS) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{X}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NPTS}$, must contain the mesh points as used by the PDE routine.

6:     XP(INTPTS) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{XP}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{INTPTS}$, must contain the spatial interpolation points.

Constraint: $\mathbf{X}\left(1\right)\le \mathbf{XP}\left(1\right)<\mathbf{XP}\left(2\right)<\cdots <\mathbf{XP}\left(\mathbf{INTPTS}\right)\le \mathbf{X}\left(\mathbf{NPTS}\right)$.

7:     INTPTS – INTEGERInput

On entry: the number of interpolation points.

Constraint: $\mathbf{INTPTS}\ge 1$.

8:     ITYPE – INTEGERInput

On entry: specifies the interpolation to be performed.

$\mathbf{ITYPE}=1$

The solutions at the interpolation points are computed.

$\mathbf{ITYPE}=2$

Both the solutions and their first derivatives at the interpolation points are computed.

Constraint: $\mathbf{ITYPE}=1$ or $2$.

9:     UP(NPDE,INTPTS,ITYPE) – REAL (KIND=nag_wp) arrayOutput

On exit: if $\mathbf{ITYPE}=1$, $\mathbf{UP}\left(\mathit{i},\mathit{j},1\right)$, contains the value of the solution $U_{\mathit{i}}\left(x_{\mathit{j}},t_{\mathrm{out}}\right)$, at the interpolation points $x_{\mathit{j}}=\mathbf{XP}\left(\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{INTPTS}$ and $\mathit{i}=1,2,\dots ,\mathbf{NPDE}$.

If $\mathbf{ITYPE}=2$, $\mathbf{UP}\left(\mathit{i},\mathit{j},1\right)$ contains $U_{\mathit{i}}\left(x_{\mathit{j}},t_{\mathrm{out}}\right)$ and $\mathbf{UP}\left(\mathit{i},\mathit{j},2\right)$ contains $\frac{\partial U_{\mathit{i}}}{\partial x}$ at these points.

10:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{ITYPE}\ne 1$ or $2$,
or	$\mathbf{INTPTS}<1$,
or	$\mathbf{NPDE}<1$,
or	$\mathbf{NPTS}<3$,
or	$\mathbf{M}\ne 0$, $1$ or $2$,
or	the mesh points $\mathbf{X}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NPTS}$, are not in strictly increasing order.

$\mathbf{IFAIL}=2$

On entry, the interpolation points $\mathbf{XP}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{INTPTS}$, are not in strictly increasing order.

$\mathbf{IFAIL}=3$

You are attempting extrapolation, that is, one of the interpolation points $\mathbf{XP}\left(i\right)$, for some $i$, lies outside the interval [$\mathbf{X}\left(1\right),\mathbf{X}\left(\mathbf{NPTS}\right)$]. Extrapolation is not permitted.

7  Accuracy

8  Further Comments

9  Example