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Math Help - lotka-volterra equations?? Euler

  1. #1
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    lotka-volterra equations?? Euler

    Hey guys
    I am working on oscillation and have been looking at the lotka-volterra equations. I may have misunderstood the question, but this is the equations:

    y'= Ax-Bxy
    y'=-Cy+Dxy

    Can read quick about it here:http://mathworld.wolfram.com/images/...s/Inline11.gif

    I may have misunderstood, but i am supposed to find a numerical solution using Eulers method. Well, give an example of it. Can anyone help me pls. Really desperate.

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  2. #2
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    Re: lotka-volterra equations?? Euler

    Hey MathNoobMisc.

    Eulers method in general is just a taylor expansion of a function involving the initial condition and the derivative.

    We know that the first two taylor series terms are f(x) = f(a) + (x-a)*f'(a).

    If we have a system of equations, we replace x's and a's with vectors where f'(a) is a linear object (i.e a nxn matrix for system of n equations) and our Euler up-date becomes:

    f(x) = f(a) + C*(x-a) where a = [a1,a2,...,an] and x = [x1,x2,....,xn] and C is nxn derivative evaluated at vector a.

    What computational tools do you have? Do you have MATLAB or the open source version Octave (and GUIOctave)?
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