&&&&&&& matlab &&&&&&&

Your goal in this problem is to implement a similar function for the fourth-order Runge-Kutta (RK4) scheme discussed in class (see also Section 7.4 from NCM). (a) Implement a general RK4 function and name it rk4 for solving initial value problems of the form (1). Use the same inputs as we did for the modmidpoint.m and modtrapezoidal functions.

inputs:

f = @(t,y) -(1 + t + t.^2) - (2*t+1).*y - y.^2; t0 = 0; tf = 3; y0 = -1/2; N = 30;

y'(t) = f(t, y(t)), t > to, y(to) = yo