@Article{IJNAM-13-753,
author = {N. Hurl, W. Layton, Y. Li and M. Moraiti},
title = {The Unstable Mode in the Crank-Nicolson Leap-Frog Method is Stable},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {5},
pages = {753--762},
abstract = {This report proves that under the time step condition Δt|Λ| ‹ 1 (|⋅| = Euclidean
norm) suggested by root condition analysis and necessary for stability, all modes of the Crank-
Nicolson Leap-Frog (CNLF) approximate solution to the system
\frac{du}{dt}+ Au + Λu = 0; for t > 0 and u(0) = u_0;
where A + A^T is symmetric positive definite and Λ is skew symmetric, are asymptotically stable.
This result gives a sufficient stability condition for non-commutative A and Λ, and is proven by
energy methods. Thus, the growth, often reported in the unstable mode, is not due to systems
effects and its explanation must be sought elsewhere.},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/463.html}
}