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class FirstOrderPDE extends Error

The FirstOrderPDE 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: FunctionS2S, 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 end-points 0 and 'xm'

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  15. 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

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  1. def finalize(): Unit
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