dev.nm.analysis.differentialequation.pde.finitedifference

Interface PDESolutionTimeSpaceGrid1D

public interface PDESolutionTimeSpaceGrid1D

A solution to an one-dimensional PDE, which is applicable to methods which produce the solution as a grid of time and space. The valid index ranges are 0 ≤ k ≤ m and 0 ≤ j ≤ n+1, where k=0 is the initial condition and the values at the boundaries are at j=0 and j=n+1 respectively.

Coordinates are not arbitrary evaluation points

The arguments are integer grid indices, not physical time or position. Use t(int) and x(int) to recover the coordinates of a stored point. This interface does not interpolate between grid points.

Boundary coordinates can be valid even when boundary solution values are unsupported by a particular solver. In particular, Crank-Nicolson for the one-dimensional heat equation stores interior solution values only. Consult the producing solver rather than assuming every coordinate has a stored u value.

Method Summary

Modifier and Type	Method and Description
int	M() Gets the number of interior time-axis grid points in the solution.
int	N() Gets the number of interior space-axis grid points in the solution.
double	t(int m) Gets the value on the time axis at index k.
double	u(int m, int n) Gets the value of the grid point at (tm, xn).
double	x(int n) Gets the value on the space axis at index j.

Method Detail

u

double u(int m,
         int n)

Gets the value of the grid point at (t_m, x_n).

Parameters:

m - the index along the time axis

n - the index along the space axis

Returns:

the value at that point

t

double t(int m)

Gets the value on the time axis at index k.

Parameters:

m - the index of the grid point

Returns:

\(t_{m}\)

x

double x(int n)

Gets the value on the space axis at index j.

Parameters:

n - the index of the grid point

Returns:

\(x_{n}\)

M

int M()

Gets the number of interior time-axis grid points in the solution.

Returns:

the number of solution grid points along the time-axis

N

int N()

Gets the number of interior space-axis grid points in the solution.

Returns:

the number of solution grid points along the space-axis