Computational Methods In Nonlinear Analysis
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| Author | : Ioannis K. Argyros |
| Publisher | : World Scientific |
| Total Pages | : 592 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 9814405833 |
The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.
| Author | : Zakia Hammouch |
| Publisher | : Springer Nature |
| Total Pages | : 249 |
| Release | : 2020-11-13 |
| Genre | : Technology & Engineering |
| ISBN | : 3030622991 |
This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, time-fractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multi-orthogonal projections and generalized continued fractions. The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.
| Author | : Ahmed K. Noor |
| Publisher | : Elsevier |
| Total Pages | : 472 |
| Release | : 2014-05-20 |
| Genre | : Mathematics |
| ISBN | : 1483145646 |
Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.
| Author | : John R. Hauser |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1013 |
| Release | : 2009-03-24 |
| Genre | : Technology & Engineering |
| ISBN | : 1402099207 |
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 | : Sören Bartels |
| Publisher | : Springer |
| Total Pages | : 394 |
| Release | : 2015-01-19 |
| Genre | : Mathematics |
| ISBN | : 3319137972 |
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
| Author | : Roland Glowinski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 506 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 3662126133 |
This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, and nonlinear least square methods are all covered in detail, as are many applications. This volume is a classic in a long-awaited softcover re-edition.
| Author | : A. Cuyt |
| Publisher | : Elsevier |
| Total Pages | : 289 |
| Release | : 1987-03-01 |
| Genre | : Computers |
| ISBN | : 0080872476 |
While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.
| Author | : Holger Kantz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 339 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 364271949X |
This book is more than a standard proceedings volume, although it is an almost direct result of the workshop on "Nonlinear Analysis of Physiologi cal Time Series" held in Freital near Dresden, Germany, in October 1995. The idea of the meeting was, as for previous meetings devoted to related topics, such as the conference on dynamical diseases held near Montreal in February 1994 (see CHAOS Vol. 5(1), 1995), to bring together experts on the techniques of nonlinear analysis and the theory of chaos and applicants from the most fascinating field where such methods could potentially be useful: the life sciences. The former group consisted mainly of physicists and mathe maticians, the latter was represented by physiologists and medical researchers and practitioners. Many aspects of this workshop were unusual and not previously expe rienced. Also, the hosting institution, the Max Planck Institute for Physics of Complex Systems (MPIPKS), at this time was brand new. The organiz ers' rather unconventional intention was to bring specialists of both groups together to really work together. Therefore, there was an excessive availabil ity of computers and the possibility to numerically study time series data sets practitioners had supplied from their own fields, e. g. electrocardiogram (ECG) data, electroencephalogram (EEG) data, data from the respiratory system, from human voice, human posture control, and several others. These data formed a much stronger link between theoreticians and applicants than any of the common ideas.
| Author | : J. E. Dennis, Jr. |
| Publisher | : SIAM |
| Total Pages | : 394 |
| Release | : 1996-12-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971200 |
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
| Author | : Curtis R. Vogel |
| Publisher | : SIAM |
| Total Pages | : 195 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898717574 |
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
