NAG Library Function Document

nag_pde_interp_1d_fd (d03pzc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{npde}$ – IntegerInput

On entry: the number of PDEs.

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

2:    $\mathbf{m}$ – IntegerInput

On entry: the coordinate system used. If the call to nag_pde_interp_1d_fd (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 nag_pde_interp_1d_fd (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 doubleInput

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:    $\mathbf{npts}$ – IntegerInput

On entry: the number of mesh points.

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

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

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 doubleInput

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:    $\mathbf{intpts}$ – IntegerInput

On entry: the number of interpolation points.

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

8:    $\mathbf{itype}$ – 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:    $\mathbf{up}\left[\mathit{dim}\right]$ – doubleOutput

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 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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, $\mathbf{intpts}\le 0$: $\mathbf{intpts}=〈\mathit{\text{value}}〉$.

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NOT_STRICTLY_INCREASING

On entry, interpolation points xp badly ordered: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{xp}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{xp}\left[\mathit{J}-1\right]=〈\mathit{\text{value}}〉$.

On entry, mesh points x badly ordered: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{x}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left[\mathit{J}-1\right]=〈\mathit{\text{value}}〉$.

7

Accuracy

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Parallelism and Performance

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Further Comments

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Example