Math 6610 • Analysis of Numerical Methods I

{Convergence of Linear Multistep Method}

Consider the method
\[
  y_{n+2}-2y_{n+1}+y_n
  =
  \frac{h}{2}\left(f(t_{n+2},y_{n+2})-f(t_n,y_n)\right)
\]
Apply the method to the scalar IVP \(y'=y\), \(y(0)=1\) and solve exactly the
resulting difference equation, considering the starting values to be
\(y_0=y_1=1\). Show theoretically that the numerical solution does not converge
as \(h\to0\) and \(n\to\infty\).

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