NAG Library Function Document

nag_pde_interp_1d_fd (d03pzc)

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

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

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

4:     npts – IntegerInput

On entry: the number of mesh points.

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

5:     x[npts] – 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:     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.

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:     intpts – IntegerInput

On entry: the number of interpolation points.

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

8:     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:     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.

10:   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

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.

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

8  Parallelism and Performance

9  Further Comments

10  Example