dev.nm.analysis.differentialequation.pde.finitedifference.elliptic.dim2

Class PoissonEquation2D

java.lang.Object

dev.nm.analysis.differentialequation.pde.finitedifference.elliptic.dim2.PoissonEquation2D

All Implemented Interfaces:

PDE

public class PoissonEquation2D
extends Object
implements PDE

Poisson's equation is an elliptic PDE that takes the following general form. \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = f(x, y) \] with Dirichlet boundary conditions: \[ u(0, y) = g(0, y) \\ u(a, y) = g(a, y) \\ u(x, 0) = g(x, 0) \\ u(x, b) = g(x, b) \] assuming that the domain of the independent variables is a rectangular region in the x-y plane.

Note that LaPlace's equation emerges as a special case when \(f(x, y) = 0\).

See Also:

Wikipedia: Poisson's equation

Constructor Summary

Constructors

Constructor and Description
PoissonEquation2D(double a, double b, BivariateRealFunction f, BivariateRealFunction g) Constructs a Poisson's equation problem.

Method Summary

Modifier and Type	Method and Description
double	a() Gets the width (x-axis) of the rectangular region.
double	b() Gets the height (y-axis) of the rectangular region.
double	f(double x, double y) The forcing term.
double	g(double x, double y) The boundary value function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PoissonEquation2D

public PoissonEquation2D(double a,
                         double b,
                         BivariateRealFunction f,
                         BivariateRealFunction g)

Constructs a Poisson's equation problem.

Parameters:

a - the region of interest (0, a)

b - the region of interest (0, b)

f - the forcing term in the equation f(x, y)

g - the Dirichlet boundary condition g(x, y)

Method Detail

a

public double a()

Gets the width (x-axis) of the rectangular region.

Returns:

the x size of the region

b

public double b()

Gets the height (y-axis) of the rectangular region.

Returns:

the y size of the region

f

public double f(double x,
                double y)

The forcing term.

Parameters:

x - the first independent variable

y - the second independent variable

Returns:

f(x, y), the forcing function

g

public double g(double x,
                double y)

The boundary value function. These are Dirichlet (or first-type) boundary conditions.

Parameters:

x - the first independent variable

y - the second independent variable

Returns:

g(x, y), the boundary condition