Q2. The Explicit Euler Formula:

Let be an explicitly defined first order ODE with interval with spacing . Without loss of generality, assume that and for some positive integer values . The linear approximation of around and is given by

or equivalently

Stj+1=Stj+hF(tj)S(tj)

Consider the differential equation with initial condition has the exact solution . Use MATLAB code to approximate the solution to this initial value problem between 0 and 1 in increments of 0.1 using the Explicit Euler Formula. Then, plot the difference between the approximated solution and the exact solution.

dt = dt Q2. The Explicit Euler Formula: Let ds(t) = F(t,s(t)) be an explicitly defined first order ODE with interval [to,t] with spacing h. Without loss of generality, assume that t, = 0 and t; = Nh for some positive integer values N. The linear approximation of S(t) around t; and t;+1 is given by ds(t;) s(t;+1) = s(t) + (tj+1 t;) or equivalently s(t;+1) = s(t) + F(t;)S(tj) Consider the differential equation aft) = et with initial condition fo = -1 has the exact solution f(t) =-et. Use MATLAB code to approximate the solution to this initial value problem between 0 and 1 in increments of 0.1 using the Explicit Euler Formula. Then, plot the difference between the approximated solution and the exact solution. = dt