  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.
