CHEN 3201 Lecture Notes - Lecture 39: Cylindrical Coordinate System, Nonlinear System
12 Apr 2015
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1) solving a linear system can also write this as get eigenvalues get exponential eqn initial conditions y1(0) = 1 y2(0) = 2. Chen3201_numericalmethods page 1 or can invert solve the determinant of this. Chen3201_numericalmethods page 2 choose y2 = 1 --> y1 = 1. Chen3201_numericalmethods page 3 don"t know coefficients in front of eigenvectors. Chen3201_numericalmethods page 4 substitute these back into the diff eqns to check if answer is correct if it"s the same as differentiating the two things. Chen3201_numericalmethods page 7 now find the jacobian this = jacobian @ steady state. Chen3201_numericalmethods page 8 use rk4 to solve it since it"s nonlinear. Chen3201_numericalmethods page 9 this is for rk 4 min value for euler is 2. 3)do linear analysis on nonlinear system and show that it fails to do nonlinear analysis, needs cylindrical coordinates. Ss solution: x = 0, y = 0.
