nag_pde_interp_1d_fd (d03pzc) (PDF version)
d03 Chapter Contents
d03 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_pde_interp_1d_fd (d03pzc)


    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

nag_pde_interp_1d_fd (d03pzc) interpolates in the spatial coordinate the solution and derivative of a system of partial differential equations (PDEs). The solution must first be computed using one of the finite difference schemes nag_pde_parab_1d_fd (d03pcc), nag_pde_parab_1d_fd_ode (d03phc) or nag_pde_parab_1d_fd_ode_remesh (d03ppc), or one of the Keller box schemes nag_pde_parab_1d_keller (d03pec), nag_pde_parab_1d_keller_ode (d03pkc) or nag_pde_parab_1d_keller_ode_remesh (d03prc).

2  Specification

#include <nag.h>
#include <nagd03.h>
void  nag_pde_interp_1d_fd (Integer npde, Integer m, const double u[], Integer npts, const double x[], const double xp[], Integer intpts, Integer itype, double up[], NagError *fail)

3  Description

nag_pde_interp_1d_fd (d03pzc) is an interpolation function for evaluating the solution of a system of partial differential equations (PDEs), at a set of user-specified points. The solution of the system of equations (possibly with coupled ordinary differential equations) must be computed using a finite difference scheme or a Keller box scheme on a set of mesh points. nag_pde_interp_1d_fd (d03pzc) can then be employed to compute the solution at a set of points anywhere in the range of the mesh. It can also evaluate the first spatial derivative of the solution. It uses linear interpolation for approximating the solution.

4  References


5  Arguments

Note: the arguments x, m, u, npts and npde must be supplied unchanged from the PDE function.
1:     npde IntegerInput
On entry: the number of PDEs.
Constraint: npde1.
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.
Indicates Cartesian coordinates.
Indicates cylindrical polar coordinates.
Indicates spherical polar coordinates.
  • 0m2 following a finite difference function;
  • m=0 following a Keller box scheme function.
3:     u[npde×npts] const doubleInput
On entry: the PDE part of the original solution returned in the argument u by the PDE function.
Constraint: npde1.
4:     npts IntegerInput
On entry: the number of mesh points.
Constraint: npts3.
5:     x[npts] const doubleInput
On entry: x[i-1], for i=1,2,,npts, must contain the mesh points as used by the PDE function.
6:     xp[intpts] const doubleInput
On entry: xp[i-1], for i=1,2,,intpts, must contain the spatial interpolation points.
Constraint: x[0]xp[0]<xp[1]<<xp[intpts-1]x[npts-1].
7:     intpts IntegerInput
On entry: the number of interpolation points.
Constraint: intpts1.
8:     itype IntegerInput
On entry: specifies the interpolation to be performed.
The solutions at the interpolation points are computed.
Both the solutions and their first derivatives at the interpolation points are computed.
Constraint: itype=1 or 2.
9:     up[dim] doubleOutput
Note: the dimension, dim, of the array up must be at least npde×intpts×itype.
The element UPi,j,k is stored in the array element up[k-1×npde×intpts+j-1×npde+i-1].
On exit: if itype=1, UPi,j,1, contains the value of the solution Uixj,tout, at the interpolation points xj=xp[j-1], for j=1,2,,intpts and i=1,2,,npde.
If itype=2, UPi,j,1 contains Uixj,tout and UPi,j,2 contains Ui x  at these points.
10:   fail NagError *Input/Output
The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
See Section in How to Use the NAG Library and its Documentation for further information.
On entry, argument value had an illegal value.
On entry, interpolating point value with the value value is outside the x range.
On entry, intpts0: intpts=value.
On entry, itype=value.
Constraint: itype=1 or 2.
On entry, m=value.
Constraint: m=0, 1 or 2.
On entry, npde=value.
Constraint: npde>0.
On entry, npts=value.
Constraint: npts>2.
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.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
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.
On entry, interpolation points xp badly ordered: I=value, xp[I-1]=value, J=value and xp[J-1]=value.
On entry, mesh points x badly ordered: I=value, x[I-1]=value, J=value and x[J-1]=value.

7  Accuracy

See the PDE function documents.

8  Parallelism and Performance

nag_pde_interp_1d_fd (d03pzc) is not threaded in any implementation.

9  Further Comments


10  Example

See Section 10 in nag_pde_parab_1d_fd (d03pcc), nag_pde_parab_1d_fd_ode_remesh (d03ppc) and nag_pde_parab_1d_keller_ode_remesh (d03prc).

nag_pde_interp_1d_fd (d03pzc) (PDF version)
d03 Chapter Contents
d03 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016