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 - <p style="text-align: justify;">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.</p>