Solving Nonlinear Differential Equations

Mathematica is great in solving analytically linear differential equations. It is also a good companion for computing numerical solutions to non–linear equations. We attack the reduced–gravity, shallow–water equation (RSE) problem. We compare the analytical solution to our problem without friction to the numerical solution obtained either with Mathematica or via Matlab. We exploit Mathematica ability in solving systems of non-linear Ordinary Differential Equations, on the way to identify some analytical solution to RSE when friction is non-negligible