Question

急死了！！请各位大神各路神仙帮忙做以下两道题，要完整过程，满意所有分都给你了！

（1）
1. Runge-Kutta Method and Numerical Solution of ODEs
Consider Heun's method
Yn+1 = Yn +h/2[Fn + F(Tn+1; Yn + HFn)] :
(a) Show that Heun's method is an explicit two-stage Runge-Kutta method.
(b) Prove that Heun's method has order 2 with respect to h.
(c) Using MATLAB, draw the region of absolute stability of the method in the complex
plane.

(2) Multistep Method and Numerical Solution of ODEs
Consider the family of linear multistep methods Yn+1 = Yn +h/2[2(1 -a )Fn+1 + 3aFn -aFn-1] :
where  is a real parameter
(a) Analyze consistency and order of the methods as functions of , determining the
value  for which the resulting method has maximal order.
(b) Study the zero-stability of the method with  = , (for a consistent multistep
method, the root condition is equivalent to zero-stability).
(c) Using MATLAB, draw the region of absolute stability of the method with  = 
in the complex plane.

Answer 1

(1)1。龙格-库塔法和数值解的ODEsConsider Heun的methodYn + 1 = Yn + h / 2(Fn + F(Tn + 1,+ HFn Yn)]:(一)表明,Heun的方法是一种显式两级龙格-库塔法。(b)证明Heun的方法有订单2对h。(c)使用MATLAB,绘制区域的绝对稳定性的方法。(2)complexplane多步方法和数值解的家族ODEsConsider线性多步方法Yn + 1 = Yn + h / 2[2(1 -)Fn + 1 + 3 afn -aFn-1]:一个真正的参数

这个我是用的自动翻译哈，然后就是这个结果，你自己看吧

Answer 2

操，完全看不懂，你不是来挖坑的吧

Answer 3

如果是在我学数值分析时问这个问题，不在话下 如今已毕业好几年了，都忘了 哎