Using MATLAB ;

Consider the following initial value problem (IVP) dx/dt = sin (t) + x, t elementof (0, 1], x (0) = 0. Write a function for each of the following methods with the step sizes h = 1/N, N = 2, 4, ..., 128. Moreover, display the computed order of convergence. Forward Euler Backward Euler Trapezoidal Euler. Use the following formula to compute convergence rate: P_i = log (e_i/e_i - 1)/log (h_i/h_i - 1), i = 2, 3, .... Further, plot the absolute values of the errors e_i versus the step sizes h_i, in logarithmic scale. Consider the following initial value problem (IVP) dx/dt = sin (t) + x, t elementof (0, 1], x (0) = 0. Write a function for each of the following methods with the step sizes h = 1/N, N = 2, 4, ..., 128. Moreover, display the computed order of convergence. Forward Euler Backward Euler Trapezoidal Euler. Use the following formula to compute convergence rate: P_i = log (e_i/e_i - 1)/log (h_i/h_i - 1), i = 2, 3, .... Further, plot the absolute values of the errors e_i versus the step sizes h_i, in logarithmic scale