Numerical Analysis Problem

2. The interval of absolute stability can be defined more generally as those values of Ah for which all solutions of an approximation scheme remain bounded when applied to the model problem y' = \y. Use this definition in the following problem. Find the interval of absolute stability for the general R-K method of order 2, i.e., 1 Yn+1 = yn + kih +-kph, 2a 2a where ka = f(x, y), k, = f(xn+ah, yn +ak). Hint: First show that when the method is applied to the model problem y' = y, we get the difference equation Yn+1 = yn [1+hX + (hX)). (1- 2. The interval of absolute stability can be defined more generally as those values of Ah for which all solutions of an approximation scheme remain bounded when applied to the model problem y' = \y. Use this definition in the following problem. Find the interval of absolute stability for the general R-K method of order 2, i.e., 1 Yn+1 = yn + kih +-kph, 2a 2a where ka = f(x, y), k, = f(xn+ah, yn +ak). Hint: First show that when the method is applied to the model problem y' = y, we get the difference equation Yn+1 = yn [1+hX + (hX)). (1