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Numerical method to solve high order ODEs.

  1. Aug 27, 2008 #1
    here is a simplified version of my working equtions
    y''' = \frac{(y'' y+y' y) y + y'y''}{y' + y''}
    and 3 related boundary conditions, is there some hints to solve such equation numerically?

  2. jcsd
  3. Aug 27, 2008 #2


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    Homework Helper

    This might sound crazy, but note that everything here is a function of y. You may not have to resort to numerical solutions. But then again I haven't tried it out yet. Looks a little intimidating.
  4. Aug 27, 2008 #3
    in the equation,
    [tex]y = y(x) [/tex]
    The original equation are much more complex, it is not possible to get a exact analytical solution for that. What I want to learn is the general numerical method to solve such equation.
  5. Aug 27, 2008 #4


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    Science Advisor

    Let u= y'(x), v= y"(x). Then your equation is becomes
    [tex]y'= \frac{(v y+u y) y + uv}{y + v}[/tex]
    That together with y'= u and u'= v gives you three interconnected first order equations. Do, say, a 4th order Runge-Kutta, advancing the step in all three equations at the same time.
  6. Aug 27, 2008 #5
    Thats would I would suggest. Although the Adams-Moulton-Bashforth method would work as well and probably give you a little bit more accuracy. But you will need the RK4 for the first couple steps anyway.
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