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Author: Mohsen Soori
Publisher: GRIN Verlag
ISBN: 3668866546
Category : Mathematics
Languages : en
Pages : 56
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Book Description
Research Paper (postgraduate) from the year 2019 in the subject Mathematics - Applied Mathematics, , language: English, abstract: In this paper, the Variational Iteration Method (VIM) and the Homotopy Perturbation Method (HPM) are applied to solve the non-linear differential equations. The Newell-Whitehead-Segel equation, the Burgers-Huxley, the Burgers-Fisher equation, the Fitzhugh–Nagumo Equation, the Fisher Type Equation are studied in different chapters and exact solutions are also obtained. A comparison is made between obtained results in finding the exact solution of the equation in order to present precision of the methods. The results prove capability and great potential of the methods as effective algorithms in order to obtain the exact solution of non-linear differential equations.
Author: Mohsen Soori
Publisher: GRIN Verlag
ISBN: 3668866546
Category : Mathematics
Languages : en
Pages : 56
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Book Description
Research Paper (postgraduate) from the year 2019 in the subject Mathematics - Applied Mathematics, , language: English, abstract: In this paper, the Variational Iteration Method (VIM) and the Homotopy Perturbation Method (HPM) are applied to solve the non-linear differential equations. The Newell-Whitehead-Segel equation, the Burgers-Huxley, the Burgers-Fisher equation, the Fitzhugh–Nagumo Equation, the Fisher Type Equation are studied in different chapters and exact solutions are also obtained. A comparison is made between obtained results in finding the exact solution of the equation in order to present precision of the methods. The results prove capability and great potential of the methods as effective algorithms in order to obtain the exact solution of non-linear differential equations.
Author: Shijun Liao
Publisher: CRC Press
ISBN: 1135438293
Category : Mathematics
Languages : en
Pages : 335
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Book Description
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.
Author: Gangwei Wang
Publisher: Frontiers Media SA
ISBN: 2832553095
Category : Science
Languages : en
Pages : 192
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Book Description
Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due to the intricacy and contingency of nonlinear problems, unified mathematical methods still remain far and few between. In this regard, the comprehensive use of symmetric methods, along with other mathematical methods, becomes an effective option to solve nonlinear problems.
Author: Mohamed Atef Helal
Publisher: Springer Nature
ISBN: 1071624571
Category : Science
Languages : en
Pages : 483
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Book Description
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
Author: Terry E. Moschandreou
Publisher: BoD – Books on Demand
ISBN: 1789231566
Category : Mathematics
Languages : en
Pages : 184
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Book Description
The editor has incorporated contributions from a diverse group of leading researchers in the field of differential equations. This book aims to provide an overview of the current knowledge in the field of differential equations. The main subject areas are divided into general theory and applications. These include fixed point approach to solution existence of differential equations, existence theory of differential equations of arbitrary order, topological methods in the theory of ordinary differential equations, impulsive fractional differential equations with finite delay and integral boundary conditions, an extension of Massera's theorem for n-dimensional stochastic differential equations, phase portraits of cubic dynamic systems in a Poincare circle, differential equations arising from the three-variable Hermite polynomials and computation of their zeros and reproducing kernel method for differential equations. Applications include local discontinuous Galerkin method for nonlinear Ginzburg-Landau equation, general function method in transport boundary value problems of theory of elasticity and solution of nonlinear partial differential equations by new Laplace variational iteration method. Existence/uniqueness theory of differential equations is presented in this book with applications that will be of benefit to mathematicians, applied mathematicians and researchers in the field. The book is written primarily for those who have some knowledge of differential equations and mathematical analysis. The authors of each section bring a strong emphasis on theoretical foundations to the book.
Author: Chu-Hui He
Publisher: Frontiers Media SA
ISBN: 2832539637
Category : Science
Languages : en
Pages : 132
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Book Description
The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.
Author: Hemen Dutta
Publisher: Springer Nature
ISBN: 3030391124
Category : Technology & Engineering
Languages : en
Pages : 341
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Book Description
This book gathers original research papers presented at the 4th International Conference on Computational Mathematics and Engineering Sciences, held at Akdeniz University, Antalya, Turkey, on 20–22 April 2019. Focusing on computational methods in science, mathematical tools applied to engineering, mathematical modeling and new aspects of analysis, the book discusses the applications of mathematical modelling in areas such as health science, engineering, computer science, social science, and economics. It also describes a wide variety of analytical, computational, and numerical methods. The conference aimed to foster cooperation between students and researchers in the areas of computational mathematics and engineering sciences, and provide a platform for them to share significant research ideas. This book is a valuable resource for graduate students, researchers and educators interested in the mathematical tools and techniques required for solving various problems arising in science and engineering, and understanding new methods and uses of mathematical analysis.
Author: J. A. Tenreiro Machado
Publisher: Springer Science & Business Media
ISBN: 3319014110
Category : Technology & Engineering
Languages : en
Pages : 433
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Book Description
Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.
Author:
Publisher: Academic Press
ISBN: 0128149973
Category : Technology & Engineering
Languages : en
Pages : 388
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Book Description
Advances and Applications of Partitioning Bioreactors, Volume 54, presents an updated reference in the field of partitioning bioreactors, addressing the relevance of kinetic determination, cell deactivation and transport phenomena from an engineering point-of-view. Topics covered in this new release include Mass transport phenomena in partitioning bioreactors, Modelling and design of partitioning bioreactors, Population balances for partitioning bioreactors, Solid-liquid partitioning bioreactors for industrial wastewater treatment, Multiphase bioreactors in the Food Industry, Multiphase bioreactors in the pharmaceutical industry, Biological treatment of gas pollutants in partitioning bioreactors, Hydrocarbon biodegradation using airlift bioreactors, and more. - Contains contributions from experts in their respective areas - Updated, state-of-the-art work on partitioning bioreactors
Author: Vasile Marinca
Publisher: Springer Science & Business Media
ISBN: 364222735X
Category : Technology & Engineering
Languages : en
Pages : 403
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Book Description
This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.
