Problem # 3 only

Consider the IVPs dy =f(t,y), a t b, y(a)=?. d 120stsi, 0)1 1. Write a Matlab function called RK2 that solve(1) using Order 2 Runge-Kutta method. Use this method to solve the IVP (2) with N- 20,50, 100. Call y0, yl, y2, the three results and plot the three solutions on the same graph. Make a loglog plot of absolute error att 1 versus the number of intervals for all three methods on the same plot. Compare the solution at t = 1 with the exact solution at t = 1 Create Err a vector that stores the absolute error of the three solutions at t = 1. Comment on the result (is the method converging or not, etc.) using % 2. Write a Matlab function called RK4 that solve (1) using Order 4 Runge-Kutta method. Use this method to solve the IVP (2) with N = 20.50, 100, Call y 3, y 4, y 5, the three results and plot the three solutions on the same graph. Make a log log plot of absolute error at t = 1 versus the number of ?ntervals for all three methods on the same plot. Compare the solution at t-1 with the exact solution at t-1 Create Err 1 a vector that stores the absolute error of the three solutions at t 1, Comment on the result (is the method converging or not, etc.) using 3. Write a Matlab function called AB4 that solve (1) using four-step Adams-Bashforth method. You may use your textbook to get the coefficients. Use this method to solve the IVP (2) with N- 20,50, 100. Call y6, y7, y8, the three results and plot the three solutions on the same graph. Notice: be careful on how to evaluate the first stepMake a loglog plot of absolute error at 1 versus the number of intervals for all three methods on the same plot. Compare the solution at t = 1 with the exact solution at t = 1. Create Err2 a vector that stores the absolute error of the three solutions at t = 1, Comment on the result (is the method converging or not, etc.) using %