Convergence of a multi-step process

40 Views Asked by At

We have the linear multi-step process

$-y_k-y_{k+1}+y_{k+2}+y_{k+3}=4hf(t_k,y_k)$

for the initial value problem $y'(t)=f(t,y(t)), y(0)=0$

Show that for $f=0$ and $y_0=y_1=y_2=0$ converges the process.

Sorry for all the questions lately, but I really want to understand this topic, but here I am lost again, because I do not know what $y_0, y_1$ and $y_2$ mean here.

What do I have to do, to show convergence?

Hints are apprechiated. Thanks in advance.