Optimal Homotopy Asymptotic Method
Download Optimal Homotopy Asymptotic Method PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Optimal Homotopy Asymptotic Method book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
The Optimal Homotopy Asymptotic Method
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Optimal Homotopy Asymptotic Method
Author: Muhammad Idrees
language: de
Publisher: LAP Lambert Academic Publishing
Release Date: 2012-06
The objective of this work is to use Optimal Homotopy Asymptotic Method (OHAM), a new semi-analytic approximating technique, for solving linear and nonlinear initial and boundary value problems. The semi analytic solutions of nonlinear fourth order, eighth order, special fourth order and special sixth order boundary-value problems are computed using OHAM. Successful application of OHAM for squeezing flow is a major task in this study. This work also investigates the effectiveness of OHAM formulation for Partial Differential Equations (Wave Equation and Korteweg de Vries). OHAM is independent of the free parameter and there is no need of the initial guess as there is in Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM). OHAM works very well with large domains and provides better accuracy at lower-order of approximations. Moreover, the convergence domain can be easily adjusted. The results are compared with other methods like HPM, VIM and HAM, which reveal that OHAM is effective, simpler, easier and explicit.
Fuzzy Fractional Differential Operators and Equations
Author: Tofigh Allahviranloo
language: en
Publisher: Springer Nature
Release Date: 2020-06-15
This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.