NAG Library Function Document

nag_pde_interp_1d_coll (d03pyc)

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:    $\mathbf{u}\left[\mathbf{npde}\times \mathbf{npts}\right]$ – 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 function nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).

3:    $\mathbf{nbkpts}$ – IntegerInput

On entry: the number of break-points.

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

4:    $\mathbf{xbkpts}\left[\mathbf{nbkpts}\right]$ – const doubleInput

On entry: $\mathbf{xbkpts}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{nbkpts}$, must contain the break-points as used by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).

Constraint: $\mathbf{xbkpts}\left[0\right]<\mathbf{xbkpts}\left[1\right]<\cdots <\mathbf{xbkpts}\left[\mathbf{nbkpts}-1\right]$.

5:    $\mathbf{npoly}$ – IntegerInput

On entry: the degree of the Chebyshev polynomial used for approximation as used by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).

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

6:    $\mathbf{npts}$ – IntegerInput

On entry: the number of mesh points as used by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).

Constraint: $\mathbf{npts}=\left(\mathbf{nbkpts}-1\right)\times \mathbf{npoly}+1$.

7:    $\mathbf{xp}\left[\mathbf{intpts}\right]$ – 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.

Constraints:

• $\mathbf{xbkpts}\left[0\right]\le \mathbf{xp}\left[0\right]<\mathbf{xp}\left[1\right]<\cdots <\mathbf{xp}\left[\mathbf{intpts}-1\right]\le \mathbf{xbkpts}\left[\mathbf{nbkpts}-1\right]$;
• if $\mathbf{itype}=2$, $\mathbf{xp}\left[\mathit{i}-1\right]\ne \mathbf{xbkpts}\left[\mathit{j}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{intpts}$ and $\mathit{j}=2,3,\dots ,\mathbf{nbkpts}-1$.

8:    $\mathbf{intpts}$ – IntegerInput

On entry: the number of interpolation points.

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

9:    $\mathbf{itype}$ – 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:  $\mathbf{up}\left[\mathit{dim}\right]$ – 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.

11:  $\mathbf{rsave}\left[\mathbf{lrsave}\right]$ – doubleCommunication Array

The array rsave contains information required by nag_pde_interp_1d_coll (d03pyc) as returned by nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc). The contents of rsave must not be changed from the call to nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc). Some elements of this array are overwritten on exit.

12:  $\mathbf{lrsave}$ – IntegerInput

On entry: the size of the workspace rsave, as in nag_pde_parab_1d_coll (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc).

13:  $\mathbf{fail}$ – 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

Extrapolation is not allowed.

NE_INCOMPAT_PARAM

On entry, $\mathbf{itype}=2$ and at least one interpolation point coincides with a break-point, i.e., interpolation point no $〈\mathit{\text{value}}〉$ with value $〈\mathit{\text{value}}〉$ is close to break-point $〈\mathit{\text{value}}〉$ with value $〈\mathit{\text{value}}〉$.

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, $\mathbf{nbkpts}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nbkpts}\ge 2$.

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

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

NE_INT_3

On entry, $\mathbf{npts}=〈\mathit{\text{value}}〉$, $\mathbf{nbkpts}=〈\mathit{\text{value}}〉$ and $\mathbf{npoly}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npts}=\left(\mathbf{nbkpts}-1\right)\times \mathbf{npoly}+1$.

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

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 $\mathbf{xp}\left[\mathit{J}-1\right]=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example