naginterfaces.library.pde.dim1_​parab_​fd_​interp¶

naginterfaces.library.pde.dim1_parab_fd_interp(m, u, x, xp, itype)[source]

dim1_parab_fd_interp 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 dim1_parab_fd(), dim1_parab_dae_fd() or dim1_parab_remesh_fd(), or one of the Keller box schemes dim1_parab_keller(), dim1_parab_dae_keller() or dim1_parab_remesh_keller().

For full information please refer to the NAG Library document for d03pz

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/d03/d03pzf.html

Parameters
mint

The coordinate system used. If the call to dim1_parab_fd_interp follows one of the finite difference functions then must be the same argument as used in that call. For the Keller box scheme only Cartesian coordinate systems are valid and so must be set to zero. No check will be made by dim1_parab_fd_interp in this case.

Indicates Cartesian coordinates.

Indicates cylindrical polar coordinates.

Indicates spherical polar coordinates.

ufloat, array-like, shape

The PDE part of the original solution returned in the argument by the PDE function.

xfloat, array-like, shape

, for , must contain the mesh points as used by the PDE function.

xpfloat, array-like, shape

, for , must contain the spatial interpolation points.

itypeint

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.

Returns
upfloat, ndarray, shape

If , , contains the value of the solution , at the interpolation points , for , for .

If , contains and contains at these points.

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: , or .

(errno )

On entry, , , and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, , , and .

Constraint: .

(errno )

On entry, interpolating point with the value is outside the range.

Notes

dim1_parab_fd_interp 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. dim1_parab_fd_interp 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.