TY - CHAP AU - Motsa Sandile Sydney AU - Samuel Felix Mutua AU - Shateyi Stanford ED - Dongbin Lee ED - Tim Burg ED - Christos Volos Y1 - 2016-10-19 PY - 2016 T1 - Solving Nonlinear Parabolic Partial Differential Equations Using Multidomain Bivariate Spectral Collocation Method N2 - The book consists mainly of two parts: Chapter 1 - Chapter 7 and Chapter 8 - Chapter 14. Chapter 1 and Chapter 2 treat design techniques based on linearization of nonlinear systems. An analysis of nonlinear system over quantum mechanics is discussed in Chapter 3. Chapter 4 to Chapter 7 are estimation methods using Kalman filtering while solving nonlinear control systems using iterative approach. Optimal approaches are discussed in Chapter 8 with retarded control of nonlinear system in singular situation, and Chapter 9 extends optimal theory to H-infinity control for a nonlinear control system.Chapters 10 and 11 present the control of nonlinear dynamic systems, twin-rotor helicopter and 3D crane system, which are both underactuated, cascaded dynamic systems. Chapter 12 applies controls to antisynchronization/synchronization in the chaotic models based on Lyapunov exponent theorem, and Chapter 13 discusses developed stability analytic approaches in terms of Lyapunov stability. The analysis of economic activities, especially the relationship between stock return and economic growth, is presented in Chapter 14. BT - Nonlinear Systems SP - Ch. 1 UR - https://doi.org/10.5772/64600 DO - 10.5772/64600 SN - 978-953-51-2715-4 PB - IntechOpen CY - Rijeka Y2 - 2024-03-28 ER -