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Math Help - Finding an approximate solution

  1. #1
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    Finding an approximate solution

    Given the equation dy/dt= t-(y^2) I have to compute 2 approximate solutions corresponding to Delta t= 1 and Delta t= 0.5 on [0,1] We are given parameter of y(0)=1

    I don't believe it is separable and I'm confused as to how to begin.
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  2. #2
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    Re: Finding an approximate solution

    The equation dy/dt= t-(y^2) is a Riccati equation. Using the classical method for solving this kind of ODE leads to the formal solution, which involves special functions (Airy or particular Bessel functions). But this is not what is asked for in the wording of the problem.
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  3. #3
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    Re: Finding an approximate solution

    Try Euler's Method (Link).
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  4. #4
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    Re: Finding an approximate solution

    You are asked for approximate solutions, so what numerical methods have you been taught ?
    Euler and improved Euler tend to come first, then perhaps Taylor and Runge-Kutta.
    Which ?
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  5. #5
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    Re: Finding an approximate solution

    Thursday's lesson was supposed to be on Eulers method but unfortunatley the snow led to canceled class on that day. That would explain my why I didn't know where to begin, thank you, hopefully it's taught on Tuesday
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  6. #6
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  7. #7
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    Re: Finding an approximate solution

    Great link, thank you very much
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