Numerical Methods for Non-Linear Systems

This course covers the comprehensive understanding of numerical methods for non-linear system analysis. For instance, it delves into the process of solving a set of non-linear equations, including single equations and characteristic equations. The course explores the application of these methods in determining the frequency function and response of a system. It further discusses the characterization of different types of responses such as fixed point, periodic, quasi-periodic, and chaotic responses. The course concludes with an introduction to plotting the time response phase portrait, Poincare section, FFT, and Lyapunov exponents. It also introduces the logistic map and cubic logistic map, explaining how to plot them and interpret the results.