NAG Library Routine Document

D03PYF

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

On entry: the PDE part of the original solution returned in the parameter U by the routine D03PDF/D03PDA or D03PJF/D03PJA.

3:     NBKPTS – INTEGERInput

On entry: the number of break points.

Constraint: $\mathbf{NBKPTS}\ge 2$.

4:     XBKPTS(NBKPTS) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{XBKPTS}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NBKPTS}$, must contain the break points as used by D03PDF/D03PDA or D03PJF/D03PJA.

Constraint: $\mathbf{XBKPTS}\left(1\right)<\mathbf{XBKPTS}\left(2\right)<\cdots <\mathbf{XBKPTS}\left(\mathbf{NBKPTS}\right)$.

5:     NPOLY – INTEGERInput

On entry: the degree of the Chebyshev polynomial used for approximation as used by D03PDF/D03PDA or D03PJF/D03PJA.

Constraint: $1\le \mathbf{NPOLY}\le 49$.

6:     NPTS – INTEGERInput

On entry: the number of mesh points as used by D03PDF/D03PDA or D03PJF/D03PJA.

Constraint: $\mathbf{NPTS}=\left(\mathbf{NBKPTS}-1\right)\times \mathbf{NPOLY}+1$.

7:     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.

Constraints:

• $\mathbf{XBKPTS}\left(1\right)\le \mathbf{XP}\left(1\right)<\mathbf{XP}\left(2\right)<\cdots <\mathbf{XP}\left(\mathbf{INTPTS}\right)\le \mathbf{XBKPTS}\left(\mathbf{NBKPTS}\right)$;
• if $\mathbf{ITYPE}=2$, $\mathbf{XP}\left(\mathit{i}\right)\ne \mathbf{XBKPTS}\left(\mathit{j}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{INTPTS}$ and $\mathit{j}=2,3,\dots ,\mathbf{NBKPTS}-1$.

8:     INTPTS – INTEGERInput

On entry: the number of interpolation points.

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

9:     ITYPE – INTEGERInput

On entry: specifies the interpolation to be performed.

$\mathbf{ITYPE}=1$

The solution at the interpolation points are computed.

$\mathbf{ITYPE}=2$

Both the solution and the first derivative at the interpolation points are computed.

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

10:   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.

11:   RSAVE(LRSAVE) – REAL (KIND=nag_wp) arrayCommunication Array

The array RSAVE contains information required by D03PYF as returned by D03PDF/D03PDA or D03PJF/D03PJA. The contents of RSAVE must not be changed from the call to D03PDF/D03PDA or D03PJF/D03PJA. Some elements of this array are overwritten on exit.

12:   LRSAVE – INTEGERInput

On entry: the size of the workspace RSAVE, as in D03PDF/D03PDA or D03PJF/D03PJA.

13:   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	$\mathbf{NPOLY}<1$,
or	$\mathbf{NPDE}<1$,
or	$\mathbf{NBKPTS}<2$,
or	$\mathbf{INTPTS}<1$,
or	$\mathbf{NPTS}\ne \left(\mathbf{NBKPTS}-1\right)\times \mathbf{NPOLY}+1$,
or	$\mathbf{XBKPTS}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NBKPTS}$, are not ordered.

$\mathbf{IFAIL}=2$

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, or when $\mathbf{ITYPE}=2$, at least one of the interpolation points stored in XP is equal to one of the break points stored in XBKPTS.

$\mathbf{IFAIL}=3$

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

7  Accuracy

8  Further Comments

9  Example