On the stability of Forward in Time and Centred in Space (FTCS) scheme for scalar hyperbolic equation
For researchers in numerical PDEs, this work challenges a long-standing belief about FTCS stability, but the result is incremental as it only applies to specific initial data bounds.
The paper shows that the FTCS scheme for scalar hyperbolic conservation laws is conditionally stable, contrary to the known unconditional instability, by deriving bounds on initial data via a transformation to a two-point convex combination scheme.
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.