That centered choice (leapfrog method) in is very successful for small time steps fl.t
Chapter 6, Problem 29(choose chapter or problem)
That centered choice (leapfrog method) in is very successful for small time steps fl.t. But find the eigenvalues of A for fl.t = ,J2 and 2: Both matrices have IAI = 1. Compute A4 in both cases and find the eigenvectors of A. That value fl.t = 2 is at the border of instability. Time steps fl.t > 2 will lead to I A I > 1, and the powers in Un = An U 0 will explode. Note You might say that nobody would compute with fl.t > 2. But if an atom vibrates with y" = -lOOOOOOy, then fl.t > .0002 will give instability. Leapfrog has avery strict stability limit. Yn+l = Yn+3Zn andZn+1 = Zn-3Yn+1 will explode because fl.t = 3 is too large.
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