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

Class WaveEquation2D

java.lang.Object

dev.nm.analysis.differentialequation.pde.finitedifference.hyperbolic.dim2.WaveEquation2D

All Implemented Interfaces:

PDE

public class WaveEquation2D
extends Object
implements PDE

A two-dimensional wave equation is a hyperbolic PDE that takes the following form. \[ \frac{\partial^2 u}{\partial t^2} = \beta (\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}) \] with fixed boundary condition, that is, \[ u(t, 0, 0) = u(t, a, 0) = u(t, 0, b) = u(t, a, b) = 0 \] and two initial conditions, namely \(u\) and its first time derivative \(u_t\): \[ u(0, x, y) = f(x, y), 0 < x < a, 0 < y < b \\ u_t(0, x, y) = g(x, y), 0 < x < a, 0 < y < b \]

See Also:

Wikipedia: Wave equation

Constructor Summary

Constructors

Constructor and Description
WaveEquation2D(double beta, double T, double a, double b, BivariateRealFunction f, BivariateRealFunction g) Create a two-dimensional wave equation.

Method Summary

Modifier and Type	Method and Description
double	a() Get the size of the two-dimensional space along the x-axis, that is, the range of x, (0 < x < a).
double	b() Get the size of the two-dimensional space along the y-axis, that is, the range of y, (0 < y < b).
double	beta() Get the value of the wave coefficient β
double	f(double x, double y) Get the initial condition of u at the given point (x,y).
double	g(double x, double y) Get the initial condition of the time derivative of u at the given point (x,y).
double	T() Get the time period of interest, that is, the range of t, (0 < t < T).

Methods inherited from class java.lang.Object

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

Constructor Detail

WaveEquation2D

public WaveEquation2D(double beta,
                      double T,
                      double a,
                      double b,
                      BivariateRealFunction f,
                      BivariateRealFunction g)

Create a two-dimensional wave equation.

Parameters:

beta - the beta in the equation

T - the time period of interest (0, T)

a - the size of the region along the x-axis, x ∈ (0, a)

b - the size of the region along the y-axis y ∈ (0, b)

f - the initial condition of u, i.e., u(0, x, y)

g - the initial condition of the time-derivative of u, i.e., \(u_{t}(0,x,y)\)

Method Detail

beta

public double beta()

Get the value of the wave coefficient β

Returns:

the wave coefficient β

T

public double T()

Get the time period of interest, that is, the range of t, (0 < t < T).

Returns:

the time period of interest

a

public double a()

Get the size of the two-dimensional space along the x-axis, that is, the range of x, (0 < x < a).

Returns:

the size of the space along the x-axis

b

public double b()

Get the size of the two-dimensional space along the y-axis, that is, the range of y, (0 < y < b).

Returns:

the size of the space along the y-axis

f

public double f(double x,
                double y)

Get the initial condition of u at the given point (x,y).

Parameters:

x - the x-coordinate

y - the y-coordinate

Returns:

u(0, x, y)

g

public double g(double x,
                double y)

Get the initial condition of the time derivative of u at the given point (x,y).

Parameters:

x - the x-coordinate

y - the y-coordinate

Returns:

\(u_{t}(0, x, y)\)