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Math Help - [SOLVED] 1st order nonlinear system of diff.equations????

  1. #1
    crb
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    [SOLVED] 1st order nonlinear system of diff.equations????

    please have a look at the attached picture....

    please help me understand how to
    solve numerically for cases
    further away from the equilibrium point?
    I can linearize it near the equillibrium point , and solve it but i don't have a clue how to get started on points further away from the equilibrium point? (numerically)
    any help me will be appriciated, please point me in the right direction, a link to some web page would be helpful too. thank you
    Attached Thumbnails Attached Thumbnails [SOLVED] 1st order nonlinear system of diff.equations????-k4.jpg  
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  2. #2
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    Numerically, you treat it just like a single differential equation except you keep track of two sets of data simultaneously since each x and y depend on each. You could easily adapt Euler to do this, it's just twice as many variables. Could use Runge-Kutta too, again, twice as many variables. I don't see how the distance from the equililbrium points are relevant in terms of numerical methods unless some stability issues are encountered like highly oscillatory or singular. I'd suggest learning how Euler works at least, maybe Runge-Kutta if you like pain, maybe do one or two, then just use Mathematica from then on:

    Code:
    m = 10; 
    n = 10; 
    a = 100; 
    b = 5; 
    xstart = 1; 
    ystart = 1; 
    sol = NDSolve[{Derivative[1][x][t] == 
         (m/n)*(a - b*y[t]), 
        Derivative[1][y][t] == 
         (a/b)*(-m + n*x[t]), x[0] == xstart, 
        y[0] == ystart}, {x, y}, {t, 0, 10}]
    ParametricPlot[Evaluate[{x[t], y[t]} /. 
        sol], {t, 0, 10}, AspectRatio -> 1]
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  3. #3
    crb
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    thank you for ur directrion....will have a look at those numerical methods , and see what happens....
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