2.3 Introduction to Finite Difference Methods

2.3.4 Forward Time-Backward Space (FTBS)

Measurable Outcome 2.3, Measurable Outcome 2.9, Measurable Outcome 2.10

Download the code from the Section 2.3.3. Modify it to use the backward difference formula \(\delta _ x^{-}\). This method known as the Forward Time-Backward Space (FTBS) method. Using the same \(u=1, {\Delta t}= \frac{1}{1000}\) and \(\Delta x = \frac{1}{50}\) does the FTBS method exhibit the same instability as the FTCS method?

Exercise 1
Answer: It can be shown that the FTBS method is stable for the timestep chosen. The stability of the FTBS method means the solution will not grow unbounded in time.