1.8 Multi-Step Methods

1.8.4 Backwards Differentiation Exercise

Measurable Outcome 1.12, Measurable Outcome 1.15, Measurable Outcome 1.18, Measurable Outcome 1.19



Suppose we wish to simulate the ODE \(u_ t = Au\) defined by the 2-by-2 matrix \(A\) for \({\Delta t}=0.1\). For which of the following \(A\) matrices will the fourth-order accurate backwards differentiation method be eigenvalue stable?

Exercise 1



Answer: The third matrix is the only one with both eigenvalues inside of the stability region for \({\Delta t}=0.1\).