Numerical Solutions Of Realistic Nonlinear Phenomena

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Numerical Solutions of Realistic Nonlinear Phenomena

Author : J. A. Tenreiro Machado
Publisher : Springer Nature
ISBN 13 : 3030371417
Total Pages : 231 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Numerical Solutions of Realistic Nonlinear Phenomena by : J. A. Tenreiro Machado

Download or read book Numerical Solutions of Realistic Nonlinear Phenomena written by J. A. Tenreiro Machado and published by Springer Nature. This book was released on 2020-02-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.

The Optimal Homotopy Asymptotic Method

Author : Vasile Marinca
Publisher : Springer
ISBN 13 : 3319153749
Total Pages : 476 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis The Optimal Homotopy Asymptotic Method by : Vasile Marinca

Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics

Author : Mustafa Inc
Publisher : Frontiers Media SA
ISBN 13 : 2832539432
Total Pages : 160 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics by : Mustafa Inc

Download or read book New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics written by Mustafa Inc and published by Frontiers Media SA. This book was released on 2023-11-20 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws

Numerical Methods for Diffusion Phenomena in Building Physics

Author : Nathan Mendes
Publisher : Springer Nature
ISBN 13 : 3030315746
Total Pages : 253 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Numerical Methods for Diffusion Phenomena in Building Physics by : Nathan Mendes

Download or read book Numerical Methods for Diffusion Phenomena in Building Physics written by Nathan Mendes and published by Springer Nature. This book was released on 2019-11-29 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second edition of Numerical methods for diffusion phenomena in building physics: a practical introduction originally published by PUCPRESS (2016). It intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. In this reviewed edition, an innovative way to simulate energy and hydrothermal performance are presented, bringing some light on innovative approaches in the field.

Robust Numerical Methods for Singularly Perturbed Differential Equations

Author : Hans-Görg Roos
Publisher : Springer Science & Business Media
ISBN 13 : 3540344675
Total Pages : 599 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Robust Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos

Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2008-09-17 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

Numerical Methods for Singularly Perturbed Differential Equations

Author : Hans-Görg Roos
Publisher : Springer Science & Business Media
ISBN 13 : 3662032066
Total Pages : 364 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos

Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.

Nonlinear Physics with Maple for Scientists and Engineers

Author : Richard H. Enns
Publisher : Springer Science & Business Media
ISBN 13 : 1461213223
Total Pages : 674 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Physics with Maple for Scientists and Engineers by : Richard H. Enns

Download or read book Nonlinear Physics with Maple for Scientists and Engineers written by Richard H. Enns and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophy of the Text This text presents an introductory survey of the basic concepts and applied mathematical methods of nonlinear science as well as an introduction to some simple related nonlinear experimental activities. Students in engineering, phys ics, chemistry, mathematics, computing science, and biology should be able to successfully use this book. In an effort to provide the reader with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of the Maple software sys tem applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The CD-ROM provided with this book gives a wide variety of illustrative non linear examples solved with Maple. In addition, numerous annotated examples are sprinkled throughout the text and also placed on the CD. An accompanying set of experimental activities keyed to the theory developed in Part I of the book is given in Part II. These activities allow the student the option of "hands on" experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated.

Nonlinear Problems and Numerical Methods in Differential Equations and Applied Phenomena

Author : D. S. Cohen
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Nonlinear Problems and Numerical Methods in Differential Equations and Applied Phenomena by : D. S. Cohen

Download or read book Nonlinear Problems and Numerical Methods in Differential Equations and Applied Phenomena written by D. S. Cohen and published by . This book was released on 1988 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summaries of Work: Continuation - Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems; Some bifurcation diagrams for Taylor vortex flows; A Direct Method for Computing Higher Order Folds; Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders; The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations; A Multigrid Continuation Method for Elliptic Problems with Folds; Multiple Laminar Flows Through Curved Pipes; Asymptotic Boundary Conditions and Numerical Methods for Nonlinear Elliptic Problems on Unbounded Domains; Computation of Anomalous Modes in the Taylor Experiment; Equilibrium Chaos and Related Parameter Sequences; Computations of Taylor Vortex Flows Using Multigrid Continuation Methods; Complex Bifurcation From Real Paths; Diffusive Fronts of Penetrants in Glassy Polymers; Chemical Reactor Theory and Problems in Diffusion; Sorption of a Finite Amount of Swelling Solvent in a Glassy Polymer; Asymptotic Methods of Semi-Conductor Modeling; Free Boundary Problems in Controlled Release Pharmaceuticals Diffusion in Glassy Polymers; Free Boundary Problems in Controlled Release Pharmaceuticals Swelling Controlled Release; and A Mathematical Model for Stress - Driven Diffusion in Polymers. (JHD).

Self-Similarity and Beyond

Author : P.L. Sachdev
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781584882114
Total Pages : 336 pages
Book Rating : 4.8/5 (821 download)

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Book Synopsis Self-Similarity and Beyond by : P.L. Sachdev

Download or read book Self-Similarity and Beyond written by P.L. Sachdev and published by Chapman and Hall/CRC. This book was released on 2000-08-24 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents a myriad of approaches to finding exact solutions for a diversity of nonlinear problems. These include group-theoretic methods, the direct method of Clarkson and Kruskal, traveling waves, hodograph methods, balancing arguments, embedding special solutions into a more general class, and the infinite series approach. The author's approach is entirely constructive. Numerical solutions either motivate the analysis or confirm it, therefore they are treated alongside the analysis whenever possible. Many examples drawn from real physical situations-primarily fluid mechanics and nonlinear diffusion-illustrate and emphasize the central points presented. Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts, will re-discover the importance of exact solutions and find valuable additions to their mathematical toolkits.

Nonlinear Phenomena in the Ionosphere

Author : A. Gurevich
Publisher : Springer Science & Business Media
ISBN 13 : 3642876498
Total Pages : 381 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Nonlinear Phenomena in the Ionosphere by : A. Gurevich

Download or read book Nonlinear Phenomena in the Ionosphere written by A. Gurevich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear effects in the ionosphere (cross modulation of radio waves) have been known since the 1930s. Only recently, however, has the rapid increase in the power and directivity of the radio transmitters made it possible to alter the properties of the ionosphere strongly and to modify it artificially by applying radio waves. This has revealed a variety of new physical phenomena. Their study is not only of scien tific interest but also undisputedly of practical interest, and is presently progressing very rapidly. This monograph is devoted to an exposition of the present status of theoretical research on this problem. Particular attention is paid, naturally, to problems in the development of which the author himself took part. It is my pleasant duty to thank V. L. Ginzburg, L. P. Pitaevskii, V. V. Vas'kov, E. E. Tsedilina, A. B. Shvartsburg, and Va. S. Dimant for useful discussions and for valuable remarks during various stages of the work on the problem considered in this book. Contents 1. Introduction . . . . . . . . . . . . . . . . . . .

Nonlinear Dynamics

Author : Valery N. Pilipchuk
Publisher : Springer Science & Business Media
ISBN 13 : 3642127991
Total Pages : 366 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Nonlinear Dynamics by : Valery N. Pilipchuk

Download or read book Nonlinear Dynamics written by Valery N. Pilipchuk and published by Springer Science & Business Media. This book was released on 2010-05-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of “unusual” physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some “quasi impact” methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book.

Nonlinear Systems, Vol. 1

Author : Victoriano Carmona
Publisher : Springer
ISBN 13 : 3319667661
Total Pages : 428 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Nonlinear Systems, Vol. 1 by : Victoriano Carmona

Download or read book Nonlinear Systems, Vol. 1 written by Victoriano Carmona and published by Springer. This book was released on 2018-09-15 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Mathematics for Nonlinear Phenomena — Analysis and Computation

Author : Yasunori Maekawa
Publisher : Springer
ISBN 13 : 3319667645
Total Pages : 335 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Mathematics for Nonlinear Phenomena — Analysis and Computation by : Yasunori Maekawa

Download or read book Mathematics for Nonlinear Phenomena — Analysis and Computation written by Yasunori Maekawa and published by Springer. This book was released on 2017-11-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.

Variational and Topological Methods in the Study of Nonlinear Phenomena

Author : V. Benci
Publisher : Springer Science & Business Media
ISBN 13 : 9780817642785
Total Pages : 152 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Variational and Topological Methods in the Study of Nonlinear Phenomena by : V. Benci

Download or read book Variational and Topological Methods in the Study of Nonlinear Phenomena written by V. Benci and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are an outgrowth of an international conference entitled Variational and Topological Methods in the Study of Nonlinear Phe- nomena, held in Pisa in January-February 2000. Under the framework of the research project Differential Equations and the Calculus of Variations, the conference was organized to celebrate the 60th birthday of Antonio Marino, one of the leaders of the research group and a significant contrib- utor to the mathematical activity in this area of nonlinear analysis. The volume highlights recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological meth- ods. A broad range of topics is covered, including: concentration phenomena in PDEs, variational methods with applications to PDEs and physics, pe- riodic solutions of ODEs, computational aspects in topological methods, and mathematical models in biology. Though well-differentiated, the topics covered are unified through a com- mon perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on PDEs and ODEs. The volume is an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors are M. Clapp, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzan- towicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, M. del Pino, E. Sere, E. Schwartzman, P. Sintzoff, R. Turner, and I\f. Willem.

Asymptotic Methods In Nonlinear Wave Phenomena: In Honor Of The 65th Birthday Of Antonio Greco

Author : Marco Sammartino
Publisher : World Scientific
ISBN 13 : 9814475076
Total Pages : 228 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Asymptotic Methods In Nonlinear Wave Phenomena: In Honor Of The 65th Birthday Of Antonio Greco by : Marco Sammartino

Download or read book Asymptotic Methods In Nonlinear Wave Phenomena: In Honor Of The 65th Birthday Of Antonio Greco written by Marco Sammartino and published by World Scientific. This book was released on 2007-04-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena.Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.

Robust Numerical Methods for Singularly Perturbed Differential Equations

Author : Hans-G. Roos
Publisher : Springer
ISBN 13 : 9783540861973
Total Pages : 604 pages
Book Rating : 4.8/5 (619 download)

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Book Synopsis Robust Numerical Methods for Singularly Perturbed Differential Equations by : Hans-G. Roos

Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-G. Roos and published by Springer. This book was released on 2009-08-29 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

Fluid Flow Phenomena

Author : Paolo Orlandi
Publisher : Springer Science & Business Media
ISBN 13 : 9401142815
Total Pages : 369 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Fluid Flow Phenomena by : Paolo Orlandi

Download or read book Fluid Flow Phenomena written by Paolo Orlandi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the simulation of the incompressible Navier-Stokes equations for laminar and turbulent flows. The book is limited to explaining and employing the finite difference method. It furnishes a large number of source codes which permit to play with the Navier-Stokes equations and to understand the complex physics related to fluid mechanics. Numerical simulations are useful tools to understand the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transferring one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory. Two chapters on Large Eddy Simulations have been included, since this is a methodology that in the near future will allow more universal turbulence models for practical applications. The direct simulation of the Navier-Stokes equations (DNS) is simple by finite-differences, that are satisfactory to reproduce the dynamics of turbulent flows. A large part of the book is devoted to the study of homogeneous and wall turbulent flows. In the second chapter the elementary concept of finite difference is given to solve parabolic and elliptical partial differential equations. In successive chapters the 1D, 2D, and 3D Navier-Stokes equations are solved in Cartesian and cylindrical coordinates. Finally, Large Eddy Simulations are performed to check the importance of the subgrid scale models. Results for turbulent and laminar flows are discussed, with particular emphasis on vortex dynamics. This volume will be of interest to graduate students and researchers wanting to compare experiments and numerical simulations, and to workers in the mechanical and aeronautic industries.