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Math Help - Lipschitz condition

  1. #1
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    Lipschitz condition

    Hi Guys,

    I'm trying to get my head around this whole Lipschitz condition business, and while I understand the principle, I'm having trouble understanding it mathematically. I have the example IVP:

    y'(t) = t*sqrt(|y|)

    Which with y(0) = 0, fails on IVP solvers. Apparently this can be explained in terms of a Lipschitz condition, but I haven't got a clue where to start proving it.

    Any help would be greatly appreciated.

    Thanks!
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  2. #2
    MHF Contributor chisigma's Avatar
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    If we write the DE as...

    y^{'} = f(t,y) (1)

    ... we observe that for y=0 the partial derivative f_{y} has a singularity and the the Lipschitz aren't satisfied. As consequence of that the IVP...

    y^{'} = t\cdot \sqrt{|y|} , y(0)=0 (2)

    ... has more that one solution, among them y= \frac{t^{4}}{16} and y = 0...

    Kind regards

    \chi \sigma
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