Non Linear Differential Equations

Author : R. Grimshaw
Publisher : Routledge
Page : 276 pages
File Size : 54,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351428088

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Nonlinear Ordinary Differential Equations by R. Grimshaw Pdf

Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642971495

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Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst Pdf

Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Author : Dominic Jordan,Peter Smith
Publisher : OUP Oxford
Page : 540 pages
File Size : 54,7 Mb
Release : 2007-08-24
Category : Mathematics
ISBN : 9780191525995

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Nonlinear Ordinary Differential Equations by Dominic Jordan,Peter Smith Pdf

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007). Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 49,6 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

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 : Tomás Roubicek
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 42,8 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373979

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Nonlinear Partial Differential Equations with Applications by Tomás Roubicek Pdf

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 : Raimond A. Struble
Publisher : Courier Dover Publications
Page : 289 pages
File Size : 52,5 Mb
Release : 2018-01-16
Category : Mathematics
ISBN : 9780486817545

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Nonlinear Differential Equations by Raimond A. Struble Pdf

Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.

Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Page : 835 pages
File Size : 45,5 Mb
Release : 2004-06-02
Category : Mathematics
ISBN : 9781135440817

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Handbook of Nonlinear Partial Differential Equations by Andrei D. Polyanin,Valentin F. Zaitsev Pdf

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:

Author : Viorel Barbu
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 45,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9781441955425

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Nonlinear Differential Equations of Monotone Types in Banach Spaces by Viorel Barbu Pdf

This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.

Author : Harold Thayer Davis
Publisher : Unknown
Page : 590 pages
File Size : 42,9 Mb
Release : 1960
Category : Calculus
ISBN : MINN:31951D03527010I

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Introduction to Nonlinear Differential and Integral Equations by Harold Thayer Davis Pdf

Author : Donal O'Regan
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 50,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401715171

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Existence Theory for Nonlinear Ordinary Differential Equations by Donal O'Regan Pdf

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.

Author : W. F. Ames
Publisher : Academic Press
Page : 282 pages
File Size : 43,8 Mb
Release : 1968
Category : Computers
ISBN : 9780080955506

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Nonlinear Ordinary Differential Equations in Transport Processes by W. F. Ames Pdf

Nonlinear Ordinary Differential Equations in Transport Processes

Author : LUIS MANUEL. BRAGA DA COSTA CAMPOS
Publisher : Unknown
Page : 0 pages
File Size : 54,5 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 1032653728

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Non-Linear Differential Equations and Dynamical Systems by LUIS MANUEL. BRAGA DA COSTA CAMPOS Pdf

This the second book of Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-Volume Set, in the Mathematics and Physics for Science and Technology series. This book considers general first-order differential equations, including non-linear and with variable coefficients.

Author : George R. Gavalas
Publisher : Springer Science & Business Media
Page : 116 pages
File Size : 48,8 Mb
Release : 2013-03-13
Category : Mathematics
ISBN : 9783642876431

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Nonlinear Differential Equations of Chemically Reacting Systems by George R. Gavalas Pdf

In recent years considerable interest has developed in the mathe matical analysis of chemically reacting systems both in the absence and in the presence of diffusion. Earlier work has been limited to simple problems amenable to closed form solutions, but now the computer permits the numerical solution of complex systems of nonlinear differ ential equations. The numerical approach provides quantitative infor mation, but for practical reasons it must be limited to a rather narrow range of the parameters of the problem. Consequently, it is desirable to obtain broader qualitative information about the solutions by in vestigating from a more fundamental mathematical point of view the structure of the differential equations. This theoretical approach can actually complement and guide the computational approach by narrow ing down trial and error procedures, pinpointing singularities and suggesting methods for handling them. The study of the structure of the differential equations may also clarify some physical principles and suggest new experiments. A serious limitation ofthe theoretical approach is that many of the results obtained, such as the sufficient conditions for the stability of the steady state, turn out to be very conservative. Thus the theoretical and computational approaches are best used to gether for the purpose of understanding, designing, and controlling chemically reacting systems. The present monograph is intended as a contribution to the theory of the differential equations describing chemically reacting systems.

Author : V.L. Kocic,G. Ladas
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401717038

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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by V.L. Kocic,G. Ladas Pdf

Nonlinear difference equations of order greater than one are of paramount impor tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.

Author : J. David Logan
Publisher : John Wiley & Sons
Page : 416 pages
File Size : 55,6 Mb
Release : 2008-04-11
Category : Mathematics
ISBN : 9780470225950

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An Introduction to Nonlinear Partial Differential Equations by J. David Logan Pdf

Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.