MATLAB

1. Computing the solution to the transport equation Using Matlab, we want to solve numerically for the solution ux, t) to the transport equation 11 + 1 = 0 with initial data u(3, 0) given by (4.7.7). Fix Ax = 0.1 and numerically implement all three schemes (4.7.4), (4.7.5), and (4.7.6) to find the solution at t = 1 when r =1,1,2. Repeat for Ax = 0.01. Since you are doing this for three schemes, each with three different choices of r and two choices of Ar, you will end up with 3 x 3 x 2 approximations for ux, 1). Plot your results against the exact solution and make some conclusions as to the accuracy of these schemes. 1. Computing the solution to the transport equation Using Matlab, we want to solve numerically for the solution ux, t) to the transport equation 11 + 1 = 0 with initial data u(3, 0) given by (4.7.7). Fix Ax = 0.1 and numerically implement all three schemes (4.7.4), (4.7.5), and (4.7.6) to find the solution at t = 1 when r =1,1,2. Repeat for Ax = 0.01. Since you are doing this for three schemes, each with three different choices of r and two choices of Ar, you will end up with 3 x 3 x 2 approximations for ux, 1). Plot your results against the exact solution and make some conclusions as to the accuracy of these schemes