4. Write a MATLAB program which computes relative root-mean-square (RMS) error, using given formulae as follows. [25 points) ERMS rims lluex || where, RMS = (u, -us)2 + (uz - u)2 + (uz - u)2 + ... + (UN+1 - ) N and ()2 + (%)2 + ( )2 + ... + ( + 1)2 u ex N Analyze the behavior of the relative error as a function of h/L = 1/N. The best way to do it is to make a log-log plot. The error typically behaves according to the power law: In = c 6 or, login = In C + ln (@) or, logrn = log C m * log(N) Both the pre-exponent, C, and the power, m, are easily found from a log-log plot which should be close to a straight line (except for very large h). First run the program using the values given in problem 1 and use N as all the even numbers in the interval [2,40). Plot error curve against the number of division and comment on your result. Now run the program using N= 2,4,6,8,10 and use log-log plot to determine m and C. 4. Write a MATLAB program which computes relative root-mean-square (RMS) error, using given formulae as follows. [25 points) ERMS rims lluex || where, RMS = (u, -us)2 + (uz - u)2 + (uz - u)2 + ... + (UN+1 - ) N and ()2 + (%)2 + ( )2 + ... + ( + 1)2 u ex N Analyze the behavior of the relative error as a function of h/L = 1/N. The best way to do it is to make a log-log plot. The error typically behaves according to the power law: In = c 6 or, login = In C + ln (@) or, logrn = log C m * log(N) Both the pre-exponent, C, and the power, m, are easily found from a log-log plot which should be close to a straight line (except for very large h). First run the program using the values given in problem 1 and use N as all the even numbers in the interval [2,40). Plot error curve against the number of division and comment on your result. Now run the program using N= 2,4,6,8,10 and use log-log plot to determine m and C