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Volume 13, Issue 5
Data Dependent Stability of Forward in Time and Centred in Space (FTCS) Scheme for Scalar Hyperbolic Equations

R. Kumar Dubey

Int. J. Numer. Anal. Mod., 13 (2016), pp. 689-704.

Published online: 2016-09

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  • 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.

  • Keywords

Numerical oscillations, von-Neumann stability, smoothness parameter, finite difference schemes, hyperbolic conservation laws.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-689, author = {R. Kumar Dubey}, title = {Data Dependent Stability of Forward in Time and Centred in Space (FTCS) Scheme for Scalar Hyperbolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {5}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/460.html} }
TY - JOUR T1 - Data Dependent Stability of Forward in Time and Centred in Space (FTCS) Scheme for Scalar Hyperbolic Equations AU - R. Kumar Dubey JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 689 EP - 704 PY - 2016 DA - 2016/09 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/460.html KW - Numerical oscillations, von-Neumann stability, smoothness parameter, finite difference schemes, hyperbolic conservation laws. AB -

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.

R. Kumar Dubey. (2016). Data Dependent Stability of Forward in Time and Centred in Space (FTCS) Scheme for Scalar Hyperbolic Equations. International Journal of Numerical Analysis and Modeling. 13 (5). 689-704. doi:
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