(* rk3stab.wl -- linear stability for a different RK3 method *)

k1=f[t,y[t]]
k2=f[t+1/2*h,y[t]+1/2*h*k1]
k3=f[t+2/3*h,y[t]+2/9*h*k1+4/9*h*k2]
method=y[t+h]==y[t]+h*(1/4*k1+3/4*k3)
linear=method/.f->Function[{t,y},lambda*y]
Simplify[linear/.{h->1,lambda->z}]
