MATLAB

The Euler Method is the simplest of the numerical methods we cover, and as we saw in class is closely related to a Left Riemann Sum. The algorithm (in pseudo code) for Euler's Method is as follows: define f(t, y) input initial values t0 and y0 input step size h and number of steps n output t0 and y0 for j from 1 to n k1 = f(t, y) y = y + h*k1 t = t + h end output t and y. Write a script that applies Euler's Method to the initial value problem y' = 1 - t + 4Y, with y(0) = 1 on the interval [0, 2] using a step size of h = 0.01. Compare your answer to the values given in the table on p. 453. The Euler Method is the simplest of the numerical methods we cover, and as we saw in class is closely related to a Left Riemann Sum. The algorithm (in pseudo code) for Euler's Method is as follows: define f(t, y) input initial values t0 and y0 input step size h and number of steps n output t0 and y0 for j from 1 to n k1 = f(t, y) y = y + h*k1 t = t + h end output t and y. Write a script that applies Euler's Method to the initial value problem y' = 1 - t + 4Y, with y(0) = 1 on the interval [0, 2] using a step size of h = 0.01. Compare your answer to the values given in the table on p. 453