Package by.andd3dfx.math.pde.equation

Class HyperbolicEquation

java.lang.Object

by.andd3dfx.math.pde.equation.Equation

by.andd3dfx.math.pde.equation.HyperbolicEquation

public class HyperbolicEquation
extends Equation

Represents a hyperbolic partial differential equation, which typically describes wave propagation and oscillation processes. The equation has the form:

M(x,t,U)*∂²U/∂t² + L(x,t,U)*∂U/∂t = ∂U( K(x,t,U)*∂U/∂x )/∂x + V(x,t,U)*∂U/∂x + F(x,t,U)

where U = U(x,t) is the unknown function (displacement, pressure, etc.).

This is a special case of the general second-order PDE where the coefficient of the second-order time derivative (M) is one, representing the standard form of wave equations.

See Also:

• HyperbolicEquationSolver
• Equation

Constructor Summary

Constructors

Constructor	Description
HyperbolicEquation(double x1, double x2, double t2, BorderCondition leftBorderCondition, BorderCondition rightBorderCondition)	Creates a new hyperbolic partial differential equation with specified domain and boundary conditions.

Method Summary

Modifier and Type	Method	Description
double	gdU_dt0(double x)	Returns the initial condition for the time derivative ∂U/∂t at time t = 0.
double	gM(double x, double t, double U)	Returns the coefficient M(x,t,U) of the second-order time derivative term.

Methods inherited from class by.andd3dfx.math.pde.equation.Equation

gF, gK, gL, gU0, gV

Methods inherited from class java.lang.Object

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

Constructor Details

HyperbolicEquation

public HyperbolicEquation(double x1,
 double x2,
 double t2,
 BorderCondition leftBorderCondition,
 BorderCondition rightBorderCondition)

Creates a new hyperbolic partial differential equation with specified domain and boundary conditions.

Parameters:

x1 - left boundary of the spatial domain

x2 - right boundary of the spatial domain

t2 - right boundary of the temporal domain

leftBorderCondition - boundary condition at x = x1

rightBorderCondition - boundary condition at x = x2

Throws:

IllegalArgumentException - if x1 >= x2 or t2 <= 0

Method Details

gM

public double gM(double x,
 double t,
 double U)

Returns the coefficient M(x,t,U) of the second-order time derivative term. For hyperbolic equations, this coefficient is always 1, representing the standard form of wave equations.

Overrides:

gM in class Equation

Parameters:

x - spatial coordinate

t - time coordinate

U - value of the solution at (x,t)

Returns:

coefficient M(x,t,U) = 1

gdU_dt0

public double gdU_dt0(double x)

Returns the initial condition for the time derivative ∂U/∂t at time t = 0. This method should be overridden by specific hyperbolic equation types to provide the actual initial velocity or rate of change.

Parameters:

x - spatial coordinate

Returns:

initial value of ∂U/∂t(x,0)