NAG FL Interface
d03pzf (dim1_​parab_​fd_​interp)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{npde}$ – Integer Input

On entry: the number of PDEs.

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

2: $\mathbf{m}$ – Integer Input

On entry: the coordinate system used. If the call to d03pzf follows one of the finite difference routines then m must be the same argument 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: $\mathbf{u}\left(\mathbf{npde},\mathbf{npts}\right)$ – Real (Kind=nag_wp) array Input

On entry: the PDE part of the original solution returned in the argument u by the PDE routine.

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

4: $\mathbf{npts}$ – Integer Input

On entry: the number of mesh points.

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

5: $\mathbf{x}\left(\mathbf{npts}\right)$ – Real (Kind=nag_wp) array Input

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: $\mathbf{xp}\left(\mathbf{intpts}\right)$ – Real (Kind=nag_wp) array Input

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: $\mathbf{intpts}$ – Integer Input

On entry: the number of interpolation points.

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

8: $\mathbf{itype}$ – Integer Input

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: $\mathbf{up}\left(\mathbf{npde},\mathbf{intpts},\mathbf{itype}\right)$ – Real (Kind=nag_wp) array Output

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: $\mathbf{ifail}$ – 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 $-\mathbf{1}$ 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, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{x}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$, $\mathit{j}=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left(1\right)<\mathbf{x}\left(2\right)<\cdots <\mathbf{x}\left(\mathbf{npts}\right)$.

On entry, $\mathbf{intpts}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{intpts}\ge 1$.

On entry, $\mathbf{itype}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{itype}=1$ or $2$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}=0$, $1$ or $2$.

On entry, $\mathbf{npde}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npde}>0$.

On entry, $\mathbf{npts}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npts}>2$.

$\mathbf{ifail}=2$

On entry, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{xp}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$, $\mathit{j}=〈\mathit{\text{value}}〉$ and $\mathbf{xp}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left(1\right)\le \mathbf{xp}\left(1\right)<\mathbf{xp}\left(2\right)<\cdots <\mathbf{xp}\left(\mathbf{intpts}\right)\le \mathbf{x}\left(\mathbf{npts}\right)$.

$\mathbf{ifail}=3$

On entry, interpolating point $〈\mathit{\text{value}}〉$ with the value $〈\mathit{\text{value}}〉$ is outside the x range.

$\mathbf{ifail}=-99$

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.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example