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Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2024-06-19
Category : Electronic
ISBN : 9789814468169
Author : Paul Edgar Phillipson
Publisher : World Scientific
Page : 238 pages
File Size : 41,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814271608
This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions. Sample Chapter(s). Chapter 1: Theme and Contents of this Book (85 KB). Contents: Theme and Contents of this Book; Processes in closed and Open Systems; Dynamics of Molecular Evolution; Relaxation Oscillations; Order and Chaos; Reaction Diffusion Dynamics; Solitons; Neuron Pulse Propagation; Time Reversal, Dissipation and Conservation. Readership: Advanced undergraduates, graduate students and researchers in physics, chemistry, biology or bioinformatics who are interested in mathematical modeling.
Author : T.P. Dreyer
Publisher : CRC Press
Page : 302 pages
File Size : 48,9 Mb
Release : 1993-06-28
Category : Mathematics
ISBN : 0849386365
Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study. This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.
Author : Ansgar Jüngel,Raul Manasevich,Peter A. Markowich,Henrik Shahgholian
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709106099
The papers in this book originate from lectures which were held at the "Vienna Workshop on Nonlinear Models and Analysis" – May 20–24, 2002. They represent a cross-section of the research field Applied Nonlinear Analysis with emphasis on free boundaries, fully nonlinear partial differential equations, variational methods, quasilinear partial differential equations and nonlinear kinetic models.
Author : John R. Hauser
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 44,9 Mb
Release : 2009-03-24
Category : Technology & Engineering
ISBN : 9781402099205
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 51,5 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Author : Boris P. Bezruchko,Dmitry A. Smirnov
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 44,9 Mb
Release : 2010-09-05
Category : Science
ISBN : 9783642126017
Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less speci?c approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II re?ects our professional interests as physicists who spent much time to investigations in the ?eld of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as “system identi?cation” in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s- ?ciently low order can exhibit non-trivial solutions that promise suf?ciently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random in?uence (noise) or by a very high order of equations.
Author : Courtney Brown
Publisher : SAGE
Page : 121 pages
File Size : 43,6 Mb
Release : 2007-05-18
Category : Social Science
ISBN : 9781412941082
'Differential Equations: A Modeling Approach' explains the mathematics and theory of differential equations. Graphical methods of analysis are emphasized over formal proofs, making the text even more accessible for newcomers to the subject matter.
Author : Marius Ghergu,Vicentiu RADULESCU
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 53,6 Mb
Release : 2011-10-22
Category : Mathematics
ISBN : 9783642226649
The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.
Author : Daniela Lupo,Carlo Pagani,Bernhard Ruf
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 40,5 Mb
Release : 2003-09-25
Category : Mathematics
ISBN : 3764303980
A collection of research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. Classical topics of nonlinear analysis were considered, such as calculus of variations, variational inequalities, critical point theory and their use in various aspects of the study of elliptic differential equations and systems, equations of Hamilton-Jacobi, Schrödinger and Navier-Stokes, and free boundary problems. Moreover, various models were focused upon: travelling waves in supported beams and plates, vortex condensation in electroweak theory, information theory, non-geometrical optics, and Dirac-Fock models for heavy atoms.
Author : Amelie Roberts
Publisher : Willford Press
Page : 0 pages
File Size : 40,6 Mb
Release : 2023-09-19
Category : Mathematics
ISBN : 1647285119
A differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of the function at a point. There are different types of differential equations including ordinary differential equations, linear differential equations, partial differential equations, homologous differential equations, and nonlinear differential equations. These equations can also be classified based on the order and coefficients of the derivatives, which may be either constants or functions of the independent variable. Differential equations are used to model real-world situations involving change. Such equations usually involve derivatives with respect to time. In most cases, a real-life problem involves the rate of change of a variable being proportional to some function of the variable. Such situations can be conveniently modeled using differential equations. This book provides a detailed analysis of the theory and modeling of differential equations. It is appropriate for students seeking detailed information in this area of mathematics as well as for experts.
Author : Tomás Roubicek
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 47,6 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373979
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
Author : Albert C.J. Luo,Hüseyin Merdan
Publisher : Springer
Page : 205 pages
File Size : 46,9 Mb
Release : 2016-01-28
Category : Technology & Engineering
ISBN : 9783319266305
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.
Author : Daniela Lupo,Carlo Pagani,Bernhard Ruf
Publisher : Birkhäuser
Page : 268 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880879
A collection of research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. Classical topics of nonlinear analysis were considered, such as calculus of variations, variational inequalities, critical point theory and their use in various aspects of the study of elliptic differential equations and systems, equations of Hamilton-Jacobi, Schrödinger and Navier-Stokes, and free boundary problems. Moreover, various models were focused upon: travelling waves in supported beams and plates, vortex condensation in electroweak theory, information theory, non-geometrical optics, and Dirac-Fock models for heavy atoms.
Author : Anonim
Publisher : BoD – Books on Demand
Page : 264 pages
File Size : 51,9 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9781789234046
This book focuses on several key aspects of nonlinear systems including dynamic modeling, state estimation, and stability analysis. It is intended to provide a wide range of readers in applied mathematics and various engineering disciplines an excellent survey of recent studies of nonlinear systems. With its thirteen chapters, the book brings together important contributions from renowned international researchers to provide an excellent survey of recent studies of nonlinear systems. The first section consists of eight chapters that focus on nonlinear dynamic modeling and analysis techniques, while the next section is composed of five chapters that center on state estimation methods and stability analysis for nonlinear systems.
