Perturbation Methods with Applications in Science and Engineering

?lkay Bak?rta?, İlkay Bakırtaş, İlkay Bakırtaş

• Publisher: IntechOpen
• Year: 2018
• Print ISBN: 9781789842555
• eBook ISBN: 9781838816681
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.

Table of contents

• Perturbation Methods with Applications in Science and Engineering
• Contents
• Preface
• Chapter 1 Density Functional Perturbation Theory to Predict Piezoelectric Properties
• Chapter 2 Sliding-Mode Perturbation Observer-Based Sliding-Mode Control for VSC-HVDC Systems
• Chapter 3 A Formal Perturbation Theory of Carleman Operators
• Chapter 4 On Optimal and Simultaneous Stochastic Perturbations with Application to Estimation of High-Dimensional Matrix and Data Assimilation in High-Dimensional Systems
• Chapter 5 Periodic Perturbations: Parametric Systems
• Chapter 6 Mechanical Perturbations at the Working Electrode to Materials Synthesis by Electrodeposition
• Chapter 7 Application of the Method of Matched Asymptotic Expansions to Solve a Nonlinear Pseudo-Parabolic Equation: The Saturation Convection-Dispersion Equation
• Chapter 8 Perturbation Method for Solar/Infrared Radiative Transfer in a Scattering Medium with Vertical Inhomogeneity in Internal Optical Properties