Problem 2. The initial value problem y = y – y², te [0, 2], y(0) = 2 (1) has analytic solution y(t) (a) (1). The interval of absolute stability for the Euler's method is (-2,0). What is stability...

PART A

Extracted text: Problem 2. The initial value problem y = y – y², te [0, 2], y(0) = 2 (1) has analytic solution y(t) (a) (1). The interval of absolute stability for the Euler's method is (-2,0). What is stability restrictions(i.e., the estimated results have qualitative agreement with the analytic solution) on step size h using Euler's method? Assume the Euler's method is used to solve the above initial value problem (b) (-0, 0), to solve this problem, what is stability restrictions on step size h using Trapezoidal method? If we use the Trapezoidal method, whose interval of absolute stability is