Math 6610 • Analysis of Numerical Methods I

\textbf{a)} Derive a multistep method to approximate \(y'=f(t,y)\) of the form
\[
  y_{n+1}=y_n+h(b_{-1}y'_{n+1}+b_0y'_n+b_1y'_{n-1})
\]
with \(y'_j=f(t_j,y_j)\), \(t_j=t_0+jh\) by interpolating \(f(s,y(s))\) at
\(t_{n-1}\), \(t_n\), \(t_{n+1}\).

\textbf{b)} Analyze the local truncation error of this method and the consequences
regarding convergence. What would be an appropriate predictor for this method?

\textbf{c)} Discuss the region of absolute stability of this method, and the
predictor-corrector method described in part \textbf{b)}.