Problem Sheet 5 - Consistency, Convergence and Stability#
Determine whether the 2-step Adams-Bashforth Method is consistent, convergent and stable
(405)#\[\begin{equation} w_{n+1}=w_n+(\frac{3}{2}hf(t_{n},w_{n})-\frac{1}{2}hf(t_{n-1},w_{n-1})).\end{equation}\]
Determine whether the 2-step Adams-Moulton Method is consistent, convergent and stable
(406)#\[\begin{equation} w_{n+1}=w_n+\frac{5}{12}hf(t_{n+1},w_{n+1})+\frac{8}{12}hf(t_{n},w_{n})-\frac{1}{12}hf(t_{n-1},w_{n-1}).\end{equation}\]
Determine whether the linear multistep following methods are consistent, convergent and stable:
(407)#\[\begin{equation} w_{n+1}=w_{n-1}+\frac{1}{3}h[f(t_{n+1},w_{n+1})+4f(t_n,w_n)+f(t_{n-1},w_{n-1})].\end{equation}\]
(408)#\[\begin{equation} w_{n+1}=\frac{4}{3}w_{n}-\frac{1}{3}w_{n-1}+\frac{2}{3}h[f(t_{n+1},w_{n+1})]. \end{equation}\]