Let X a denote the approximation to the solution of the initial-value problem obtained using Eulers method

Question:

Let X_a denote the approximation to the solution of the initial-value problem

dx dt x t +1' x(0) = 1

obtained using Euler’s method with a step size h = 0.1, and X_b that obtained using a step size of h = 0.05. Compute the values of X_a(t) and X_b(t) for t = 0.1, 0.2, . . . . , 1.0. Compare these values with the values of x(t), the exact solution of the problem. Compute the ratio of the errors in X_a and X_b.