A first-order ODE is given as d d y t = −0 5. y The initial condition is given as y(0) = 5.0. Write a script-m file to do the following: a. Solve the differential equation by Heun’s method to obtain y values from t = 0 to t = 10. b. Use three step sizes: h = 2.0, h = 1.0, and h = 0.1. c. Plot the results obtained for the three h values on one figure, using a different color or symbol for each case. d. The exact (mathematical) solution to the problem is y = 5 exp(–0.5t). Plot the exact solution also on the same figure as the numerical results. e. From these results, what is the most appropriate step size?
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