The FTCS scheme for transport equation isQuestion 16Answera.unstableb. stablec.None of these

The FTCS (Forward Time Centered Space) scheme is a numerical method used to solve partial differential equations, particularly for transport equations. To determine its stability:

1. FTCS Scheme Overview: The FTCS scheme is based on discretizing time and space, where the derivative with respect to time is approximated using forward differences, and the spatial derivative is approximated using central differences.

2. Stability Analysis: The stability condition for the FTCS scheme can typically be assessed using the von Neumann stability analysis. For a simple linear transport equation, the condition often leads to a result depending on the spatial and temporal step sizes.

3. Conclusion: Generally, it has been shown that the FTCS scheme can lead to instability unless certain criteria are met (typically a small Courant number). As a result:

Final Answer

a. unstable