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

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.