Numerical analysis of dynamic system(Master’s degree 2020)(All calculation results or figures obtained by computer must beattached with the program codes)(2 pages in total. Test paper and answer paper shall be submittedtogetherú)1. Consider backward differentiation formula (BDF).(a) Prove that thek-step BDF method is stable if and only ifk≤6 holds.(b) Prove that thek-step BDF method isA-stable ifk= 1,2.(c) Draw the regions of absolute stability of thek-step BDF withk= 1,2,3,4,5,6, respectively.2. Try to construct 3-stage Runge Kutta method (A, b, c) of Guasstype.(a) Discuss the existence and uniqueness of the solution pro-duced by the method when it is applied toy′(t) =f(y(t)),wherefsatisfies the Lipschitz condition.(b) Verify that the method is of order 6.(c) Prove that the method is symplectic