In Class 1. Solve the following initial value ODE between t = 0 and t = 1s with y(0) = 1 with step size of 0.25s: a) Analytically b) Using Eulers method. c) Huens method d) RK Order 4. e) Compute the...

Matlab - Math assignment - Undergraduate university level


In Class 1. Solve the following initial value ODE between t = 0 and t = 1s with y(0) = 1 with step size of 0.25s: a) Analytically b) Using Eulers method. c) Huens method d) RK Order 4. e) Compute the true error at t = 1s with each method. 2. Using the RK-Hehlbeg routine below, a step size of 0.25s, compute y at t=0.25s (i.e., you need only compute 1 step), a) compute the 4th and 5th order RK results), b) use the results to obtain the approximate error at 0.25s, c) use the true value to compute the true error at 0.25s. 3. Develop a flow chart and pseudo code for computing the RK-Fehlberg solution with integral calculation of the approximate error at each time step. Take home: 4. Develop a matlab code based on Q3 and verify it for a dt=0.25s against your solution to Q2. Include the tic toc command to calculate the execution time of your code. 5. Plot the approximate error as a function of step size dt on plot of log(error) vs. step size. On the same plot include the log(error_true) as a function of step size. 6. Using the matlab solver ode45, compute the solution to the problem at t = 1s. What is the approximate and true errors at t=1s. Compare the results in terms of accuracy and computational time to the results in Q5 and discuss the differences.