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NDSolve in Mathematica with numerical function

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Avatar for sciencolic

Sciencolic (sciencolic)

I love Physics, Mathematics and Science.
Japan

  • Mathematica
    		• 0
    23 Sep 10

    The problem that I am having is like this(a forward of this post). If I define a numerical function in Mathematica:

    F[x_] := Module[{}, FindRoot[ x y == 1, {y, 1/x} ][[1,2]] ];

    As you can see that F(x) is just 1/x. However, I just would like to illustrate the point with a simple example.

    If I solve a differential equation numerically involving F(x), I would get errors:

    sol = NDSolve[{y'[x] == F[x], y[1] == 0}, y[x], {x, 1, 3}];

    Errors:

    FindRoot::srect: Value 1/x in search specification {y,1/x} is not a number or array of numbers. >>

    NDSolve::deqn: Equation or list of equations expected instead of False in the first argument {InterpolatingFunction[{{1.,3.}},<<3>>,{Automatic}][x]==1,False}. >>

    What should I do?

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    Avatar for ross_tang

    Ross Tang (ross_tang)

    Degree in Physics and Mathematics, Master in Physics
    香港

  • Mathematica
    		• 72
    23 Sep 10

    The main reason you are having this error is that, Mathematica tries to solve your equation analytically first. Therefore, it would use symbolic form x for your function, but your function can't handle it. So it is the error. You may try to define your F(x) so that it would only compute if x is a number:

    F[x_ /; NumberQ[x]] := Module[{}, FindRoot[x y == 1, {y, 1/x}][[1, 2]]];

    With this, I can solve the differential equation using NDSolve without any errors. Hope it can help you.

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