Package by.andd3dfx.math.pde.equation

Class ParabolicEquation

java.lang.Object
by.andd3dfx.math.pde.equation.Equation
by.andd3dfx.math.pde.equation.ParabolicEquation
public class ParabolicEquation extends Equation
Represents a parabolic partial differential equation, which typically describes heat conduction or mass diffusion processes. The equation has the form:

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 (temperature or concentration).

This is a special case of the general second-order PDE where the coefficient of the second-order time derivative (M) is zero, and the coefficient of the first-order time derivative (L) is one.

See Also:

  • Constructor Summary

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

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    gL(double x, double t, double U)
    Returns the coefficient L(x,t,U) of the first-order time derivative term.

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

    gF, gK, gM, gU0, gV

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • ParabolicEquation

      public ParabolicEquation(double x1, double x2, double t2, BorderCondition leftBorderCondition, BorderCondition rightBorderCondition)
      Creates a new parabolic 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

    • gL

      public double gL(double x, double t, double U)
      Returns the coefficient L(x,t,U) of the first-order time derivative term. For parabolic equations, this coefficient is always 1, representing the standard form of heat/mass transfer equations.
      Overrides:
      gL in class Equation
      Parameters:
      x - spatial coordinate
      t - time coordinate
      U - value of the solution at (x,t)
      Returns:
      coefficient L(x,t,U) = 1