Consider backward differentiation formula (BDF). Prove that the k-step BDF method is stable if and only if k≤6 holds.
1. Consider backward differentiation formula (BDF).(a) Prove that the k-step BDF method is stable if and only if k≤6 holds.(b) Prove that the k-step BDF method is A-stable if k= 1,2.(c) Draw the regions of absolute stability of the k-step BDF with k= 1,2,3,4,5,6, respectively.2. Try to construct 3-stage Runge Kutta method (A, b, c) […]