NAG CL Interface
d03pzc (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 d03pzc follows one of the finite difference functions 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 d03pzc 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 function;
• $\mathbf{m}=0$ following a Keller box scheme function.

3: $\mathbf{u}\left[\mathbf{npde}\times \mathbf{npts}\right]$ – const double Input

Note: the $\left(i,j\right)$th element of the matrix $U$ is stored in $\mathbf{u}\left[\left(j-1\right)\times \mathbf{npde}+i-1\right]$.

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

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

4: $\mathbf{npts}$ – Integer Input

On entry: the number of mesh points.

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

5: $\mathbf{x}\left[\mathbf{npts}\right]$ – const double Input

On entry: $\mathbf{x}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{npts}$, must contain the mesh points as used by the PDE function.

6: $\mathbf{xp}\left[\mathbf{intpts}\right]$ – const double Input

On entry: $\mathbf{xp}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{intpts}$, must contain the spatial interpolation points.

Constraint: $\mathbf{x}\left[0\right]\le \mathbf{xp}\left[0\right]<\mathbf{xp}\left[1\right]<\cdots <\mathbf{xp}\left[\mathbf{intpts}-1\right]\le \mathbf{x}\left[\mathbf{npts}-1\right]$.

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: $\mathbf{up}\left[\mathit{dim}\right]$ – double Output

Note: the dimension, dim, of the array up must be at least $\mathbf{npde}\times \mathbf{intpts}\times \mathbf{itype}$.

the element $\mathbf{UP}\left(i,j,k\right)$ is stored in the array element $\mathbf{up}\left[\left(k-1\right)\times \mathbf{npde}\times \mathbf{intpts}+\left(j-1\right)\times \mathbf{npde}+i-1\right]$.

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 $x_{\mathit{j}}=\mathbf{xp}\left[\mathit{j}-1\right]$, 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: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_EXTRAPOLATION

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

NE_INT

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: $\mathbf{npts}>2$.

NE_INTERNAL_ERROR

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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NE_NOT_STRICTLY_INCREASING

On entry, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{x}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$, $\mathit{j}=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left[\mathit{j}-1\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left[0\right]<\mathbf{x}\left[1\right]<\cdots <\mathbf{x}\left[\mathbf{npts}-1\right]$.

On entry, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{xp}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$, $\mathit{j}=〈\mathit{\text{value}}〉$ and $\mathbf{xp}\left[\mathit{j}-1\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left[0\right]\le \mathbf{xp}\left[0\right]<\mathbf{xp}\left[1\right]<\cdots <\mathbf{xp}\left[\mathbf{intpts}-1\right]\le \mathbf{x}\left[\mathbf{npts}-1\right]$.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example