Write a code to solve the 1-D Euler equations with the linearized Lax-Wendroff
method (or another suitable method of your choice). Use rho(x,0) = 2,
-2 < x < 0, rho(x,0) = 1, 0 < x < 2, p(x,0) = 2, -2 < x < 0, p(x,0) = 1,
0 < x < 2, v(x,0) = 0, -2 < x < 2, rho_0 = rho_1, rho_M = rho_{M-1}, m_0 =
m_1, m_M = m_{M-1}, E_0 = E_1, E_M = E_{M-1}, where m = rho * v and p =
(gamma - 1) (E - rho * v^2/2) with gamma = 1.4. Graph true and
approximate solutions for the density, velocity, and pressure at
different times t, including t = 1. Experiment with the values of M
(and hence Delta x) and Delta t.