1 Recall the test IVP y Ay and y 0 a We consider the so

Last updated: 11/9/2023

1 Recall the test IVP y Ay and y 0 a We consider the so called implicit Trapzoidal method h W 1 W 7 f t 1 W 1 f ti wi to solve the test IVP which is a stiff system a Write down the stability function Q hA for the implicit Trapzoidal method Hint Q hX is obtained by applying the implicit Trapzoidal method to the test IVP see Lec 11 Theorem 1 b For the stability function show that if hA is a real number and h 0 we have Q hA 1 c Optional For the stability function verify that for any h such that Re hA 0 we have Q hA 1 This shows the implicit trapezoidal method is A stable