Data Dependent Stability of Forward in Time and Centred in Space (FTCS) Scheme for Scalar Hyperbolic Equations
Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 689–704
Abstract
The main novelty of this note is the approach which is used to show that Forward Time and Centred in Space (FTCS) scheme is data dependent stable for scalar hyperbolic conservation laws. Note that FTCS is well known to be unconditionally unstable in von-Neumann sense. In this new approach, the ratio of consecutive gradients is used to classify the initial data region where FTCS is non-oscillatory and stable. Numerical results for 1D scalar and system test problems are given to verify the claim.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-460
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 689–704
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Numerical oscillations von-Neumann stability smoothness parameter finite difference schemes hyperbolic conservation laws.