Could you please solve me the problem below? I think that I have silver it but I am not totally sure of my thinking. Thanks in advance.

334 Chapter 6. Quantitative Methods: Numerical Solution tion 6.3 we derived the general second-order Runge - Kutta method, which includes these as special cases: the improved Euler method, Un+1 = yn + { f ( En , Un ) + f [ In+ 1, Un + hf(In, Un)]}, (8.1) and the modified Euler method, h Un + 1 = Un + hflan + ,, Un+ , f(xn, yn)]. (8.2) (a) For the test equation y' = Ay, show that the improved Euler method is strongly stable for sufficiently small h (i.e., as h - 0). For the case where A