Chapter 1 - Introduction

Abstract

Nonlinear dynamical systems are ubiquitous in science and engineering. Although linearization is often utilized to simplify the original problem, it is not applicable in some certain cases. Some dynamical phenomena in nonlinear systems are very distinctive and cannot be revealed in linear systems. Sometimes, the consideration of nonlinearity is crucial to reveal the true dynamical behaviors that the nonlinear problem must be treated as it is. In this chapter the principal aim is to introduce the various computational methods for solving nonlinear problems. Hence attention is focused on the developments of these techniques and their performance rather than investigating the unique and intriguing features of nonlinear dynamical systems. The contents of this chapter are divided into four parts, in which we discuss the weighted residual methods, the application of weighted residual methods, the finite difference methods, and the asymptotic methods.