scalation.dynamics_pde

FirstOrderPDE

class FirstOrderPDE extends Error

This class is used to solve first order partial differential equations like the Advection Equation. Let u(x, t) = concentration in a fluid with velocity v at position 0 <= x <= xm and time t > 0. Numerically solve the Advection Equation: u_t + v(x, t) * u_x = 0 with initial conditions u(x, 0) = ic(x) boundary conditions (u(0, t), u(xm, t)) = bc

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Instance Constructors

  1. new FirstOrderPDE(v: (Double, Double) ⇒ Double, dt: Double, dx: Double, xm: Double, ic: (Double) ⇒ Double, bc: (Double, Double))

    v

    the velocity field function v(x, t)

    dt

    delta t

    dx

    delta x

    xm

    the length of the column

    ic

    the initial conditions as a function of position x

    bc

    the boundary conditions as a 2-tuple for endpoints 0 and xm

Value Members

  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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  5. final def ==(arg0: Any): Boolean

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  6. final def asInstanceOf[T0]: T0

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  7. def clone(): AnyRef

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  8. final def eq(arg0: AnyRef): Boolean

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  9. def equals(arg0: Any): Boolean

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  10. def finalize(): Unit

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  11. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

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  12. final def getClass(): java.lang.Class[_]

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  13. def hashCode(): Int

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  14. final def isInstanceOf[T0]: Boolean

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  15. final def ne(arg0: AnyRef): Boolean

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  16. final def notify(): Unit

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  17. final def notifyAll(): Unit

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  18. def solve(te: Double): VectorD

    Solve for the concentration of the column at time t, returning the vector of concentration representing the concentration profile of column over its length.

    Solve for the concentration of the column at time t, returning the vector of concentration representing the concentration profile of column over its length. This method uses an explicit finite difference technique to solve the PDE. L-W is the Lax-Wendroff scheme which has second-order accuracy.

    te

    the time the solution is desired (t-end)

    See also

    math.nju.edu.cn/~qzh/numPDE.pdf

  19. final def synchronized[T0](arg0: ⇒ T0): T0

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  20. def toString(): String

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  21. final def wait(): Unit

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  22. final def wait(arg0: Long, arg1: Int): Unit

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  23. final def wait(arg0: Long): Unit

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