Solve Problem 2 only, problem 1 is listed only for reference. Please be original. Thank you!

2. (15 points) (Computer problem) Write computer code to implement the Lax-Friedrichs and Lax-Wendroff schemes for linear hyperbolic PDEs. Test your code on the PDEs in problem 1. Choose the domain a: E [5, 5]. Compare the numerical solutions to the exact solution at t = 0.5.. 1. (25 points) Consider the linear system of PDEs, .. _._ _ 14 ut+Aum0, A[4 1]. i. Show that the system is hyperbolic. ii. Write down the solution for the initial condition u($, 0) = [1, 0]T when a: 0. iii write down the upwind scheme for this system