- 3 Consider The 2 Stage Rk Method K1 F Tn Y 2 2 K2 F Tn At Y 5 6 1 Atk Yn 1 You At K 3k2 1 (71.28 KiB) Viewed 33 times
3. Consider the 2-stage RK method K1 = f(tn, y"), 2 2 K2 = f(tn + At, y" + (5) (6) 1) , atK), yn+1 = you + At(K; +3K2).
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3. Consider the 2-stage RK method K1 = f(tn, y"), 2 2 K2 = f(tn + At, y" + (5) (6) 1) , atK), yn+1 = you + At(K; +3K2).
3. Consider the 2-stage RK method K1 = f(tn, y"), 2 2 K2 = f(tn + At, y" + (5) (6) 1) , atK), yn+1 = you + At(K; +3K2). 1 (7) (a) Prove that this method is convergent to the solution of the IVP y = f(t,y), ( 0<t<T, y(0) = a (you may assume f is continuous and Lipschitz in y). (b) Find the stability function R(2) for this RK method and prove that R(2) = e* + O(23). (8) Infer from (8) the order of the method. (c) Find the interval of A-stability of this method. This is the intersection of its A-stability region S with the real (c) axis.
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