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|Title:||A posteriori error estimates for leap-frog and cosine methods for second order evolution problems|
|Authors:||Georgoulis, Emmanuil H.|
Makridakis, Charalambos G.
Virtanen, Juha M.
|Publisher:||Society for Industrial and Applied Mathematics|
|Citation:||SIAM Journal on Numerical Analysis, 2016, 54 (1), pp. 120-136|
|Abstract:||We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order a posteriori estimates controlling the time discretization error. Our analysis has been motivated by the need to provide a posteriori estimates for the popular leap-frog method (also known as Verlet's method in the molecular dynamics literature); it is extended, however, to general cosine-type second order methods. The estimators are based on a novel reconstruction of the time-dependent component of the approximation. Numerical experiments confirm similarity of the convergence rates of the proposed estimators and the theoretical convergence rate of the true error.|
|Rights:||Copyright © 2016, Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s open access archiving policy.|
|Description:||AMS Subject Headings 35L05, 37M05, 37M15, 65M60, 65N50|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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