CHEN 3201 Lecture Notes - Lecture 36: Diagonalizable Matrix, Linear Programming
12 Apr 2015
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Related to stability of numerical integration but not the same. 1st find out if it"s stable or notthen find out what happens with it. Problem we want to solve: what are the steady states, how does the system evolve to a small perturbation around the steady states. This is some nonlinear function that we solve with newton-raphson. Q2: what happens if , what happens to. Expand the right hand side as a taylor series for small b/c we"re @ steady state. Ex: do the same for eqn 2 (replace the 1"s w/ 2"s) Didn"t understand this part ignoring all higher order terms b/c we can solve the linear version. This is a linear problem that can be solved by matrix diagonalization. Calculate the eigenvalues of the jacobian at the steady state: stable re( i) <0. It"s decaying down (this means it"s stable steady state)
