3. [4 points] The differential equation, dzy 523(m L) EI=' 2; L=;EI=1;L=1, M 2 , gm) 0, y

3. [4 points] The differential equation, (12 y d'X2 (5) 2 is solved over the domain 0 x L, where L 1, using two different numerical methods: (i) Method 1, and (ii) Method 2. The predicted solution from each method is compared with the analytical solution to obtain the maximum absolute error for different grid resolutions denoted by h. Figure shows error versus h for the two methods plotted on a log-log scale. [1.5 points] What is the order of accuracy of each method? Clearly show how you calculate it. (b) [2 points] If a solution is obtained using Method 1 on a total of 101 uniformly spaced total grid points (including boundary points), approximately how many uniformly spaced grid points are needed to obtain the solution with same level of accuracy (i.e. same error) using the Method 2? Show how you estimate. (c) [0.5 point] If you are given a software (code) that allows you to choose either method, which one will you choose to solve the above problem? Why? 1 02 10 10 10 10 10 10 102 Method 1 Method 2 10 h grid spacing 10