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Semi-implicit method for ODEs?

  1. Jul 1, 2012 #1
    I have two coupled ordinary differential equations:
    [itex]\displaystyle \frac{dx}{dt} = f(y) x[/itex]
    [itex]\displaystyle \frac{dy}{dt} = s(x) y[/itex]
    To solve these equations, we generally use explicit method, but these equations are stiff equations. Therefore semi-implicit method might be a better choice.

    I'm wondering if the following discretization mathematically legitimates or not?

    [itex]\displaystyle x^{n+1} = x^n + f(y^n) x^{n+1} dt[/itex]
    [itex]\displaystyle y^{n+1} = y^n + s(x^n) y^{n+1} dt[/itex]

    The reason I do it this way is nonlinearity of [itex]f(y)[/itex] and [itex]s(x)[/itex].
    Do you have any suggestion or recommended method?
  2. jcsd
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