Integral Methods in Science and Engineering, Volume 2 by Christian Constanda Matteo Dalla Riva Pier Domenico Lamberti & Paolo Musolino

Author:Christian Constanda, Matteo Dalla Riva, Pier Domenico Lamberti & Paolo Musolino
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Definition 1

Consider a numerical solution {V i, j n } of the PIDE computed from the scheme (14.13)– (14.15) with stepsizes h 1 = Δy 1 , h 2 = Δy 2 in a rhomboid computational domain and k = Δτ. On the one hand, it is said that {V i, j n } is strongly uniformly ∥. ∥ ∞ stable, if the vector solution V n satisfies

where Υ > 0 does not depend on the stepsizes h 1 , h 2 and k.

On the other hand, it is said to be conditionally stable when Υ is obtained under a certain condition on the stepsizes.

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