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I do not know how to solve the shallow water equations in the matrix form in MATLAB. I didn't find anything useful on the internet. I have the specific mathematical equations to solve (please see the picture below) and I must write in MATLAB. If someone has examples, I would appreciate it.

$$\frac{\partial u}{\partial t} - f\nu + g \frac{\partial \eta}{\partial x} = 0$$

$$\frac{\partial \nu}{\partial t} + fu + g\frac{\partial \eta}{\partial y}=0$$

$$\frac{\partial \nu}{\partial t}+H\big(\frac{\partial u}{\partial x} + \frac{\partial \nu}{\partial y}\big)=0$$

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    $\begingroup$ Have you tried coding it yourself? What you are asking for is a solver, but you need boundary conditions and initial conditions to solve it. Try the Runge-Kutta integration in time. For your spatial derivatives, you may want a finite differencing method. mathworld.wolfram.com/Runge-KuttaMethod.html $\endgroup$ Dec 14 '16 at 0:03
  • $\begingroup$ lmgtfy.com/… $\endgroup$
    – arkaia
    Dec 14 '16 at 3:20
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    $\begingroup$ This certainly sounds like a homework question I had at university too... you learn by doing, not from someone else's work :-) $\endgroup$ Feb 5 at 15:48
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You aren't supposed to do link only answers, but that is really all this questions deserves. Did you look on Google? I did.

https://people.sc.fsu.edu/~jburkardt/m_src/shallow_water_1d/shallow_water_1d.html

http://personalpages.manchester.ac.uk/staff/paul.connolly/teaching/practicals/shallow_water_equations.html

http://sanders.eng.uci.edu/matlabcodes.html

Those were 3 of the first 9 hits on google, and they all have code examples. There is no close option due to lack of effort, but I'll give it a downvote.

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