Question. Consider the long wave equation in dimension 1: u+ uux + 9x = 0, It + (gu)r + Uzer = 0, (1) where the function u is the surface velocity of the water along z-direction and the function g is the amplitude of the surface waves, (x, t) = [0, b] x [0, T.]. The initial condition is given by 141 (x, 0) =— — 2 tanh(k (x – xQ)), 1 g(x, 0) = -₁ (+0.5u₁), Hence, the boundary conditions are written as g (0, t) = 0, g,(b, t) = 0, VIE [0, Tel. ux (0, 1) = Uxor (0, 1) = 0, ux (b, t) = Uxx (b, t) = 0. Solve the numerical solutions of u(x, t= 10), and g(x, t = 10) with = 0.01 and k = 3.5 using finite difference method.