On the stability of Forward in Time and Centred in Space (FTCS) scheme for scalar hyperbolic equation

2015/03/06 by Ritesh Kumar Dubey, Dubey, Ritesh Kumar
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1503.02629

openalex publication_date 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that Forward Time and Centred in Space (FTCS) scheme for scalar Hyperbolic Conservation Law (HCL) is unconditionally unstable. The main contribution of this work to show that FTCS is conditionally stable for HCL. A new approach is used to give bounds on the initial data profile by transforming FTCS into two point convex combination scheme. Numerical results are given in support of the claim.

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