CHEN 3201 Lecture Notes - Lecture 34: Chemical Kinetics, Diagonal Matrix, Numerical Stability
12 Apr 2015
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Use the same methods (use newton-raphson instead of newton) Ex: harmonic oscilator above thing = the system we want to solve we also have an initial condition. Analyze a linear system as an approximation for a small disturbance to a non-linear system. 2nd way actually = correct by 1st = lazy way we"ll solve using 2nd way. Since are linearly independent, then exists each one of these can be written as single eqns. Chen3201_numericalmethods page 1 is a diagonal matrix with the n eigenvalues corresponding to the eigenvectors in. The things we did before were to help us get the independent eqns and break up the matrix. Now that we know how to write a, we substitute it into the initial value problem independent of t left multiply by the inverse of x. Chen3201_numericalmethods page 4 this means that the equations for z are decoupled. You analyze the stability of each equation separately.
