NAG Library Function Document

nag_pde_interp_1d_coll (d03pyc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     npde – IntegerInput

On entry: the number of PDEs.

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

2:     u[$\mathbf{npde}\times \mathbf{npts}$] – const doubleInput

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:     nbkpts – IntegerInput

On entry: the number of break-points.

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

4:     xbkpts[nbkpts] – 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:     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:     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:     xp[intpts] – 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:     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[$\mathit{dim}$] – 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:   rsave[lrsave] – 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:   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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.

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