Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 753–762
Abstract
This report proves that under the time step condition $\bigtriangleup t|\Lambda|<1$(| $\cdot$ | = 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
$\frac{du}{dt}+ Au + \Lambda u = 0$, for $t > 0$ and $u(0) = u_0$,
where $A + A^T$ is symmetric positive definite and $\Lambda$ is skew symmetric, are asymptotically stable.
This result gives a sufficient stability condition for non-commutative $A$ and $\Lambda$, 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-463
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 753–762
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: IMEX method Crank-Nicolson Leap-Frog CNLF unstable mode computational mode.