Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

My maths are very rusty and I would need some advice. I have some experimental results obtained in an open channel and got depth-averaged velocity u(y) at different cross-sectional locations y. I tried different models but there is one I don't know how to tackle. The following one dimensional second order ODE describes the evolution of u(y):

[tex]

a^{2}-b^{2}u^{2}+c^{2} \frac{du}{dy}+e^{2}y\frac{du}{dy}+f^{2}y^{2}\frac{d^{2}u}{dy^{2}}+r^{2}y\frac{d^{2}u}{dy^{2}}

[/tex]

I tried the dsolve function in Matlab, even putting some numbers in the constants without success. I don't really need an analytical solution (is it likely there would be any?). I have the experimental results and want to adjust part of the constant r to see how some parameters affect the results. Boundary conditions are known from experiments. Do I need to discretise that equation to get a solution? How should I do that?

I really welcome any advice or suggestion.

Regards,

Ben

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# Advice on 1D second order ODE

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