Solving Nonlinear Equations with Newton's Method

Solving Nonlinear Equations with Newton's Method PDF

Author: C. T. Kelley

Publisher: SIAM

Published: 2003-01-01

Total Pages: 117

ISBN-13: 9780898718898

DOWNLOAD EBOOK →

This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Nonlinear Equations: Methods, Models and Applications

Nonlinear Equations: Methods, Models and Applications PDF

Author: Daniela Lupo

Publisher: Springer Science & Business Media

Published: 2003-09-25

Total Pages: 284

ISBN-13: 9783764303983

DOWNLOAD EBOOK →

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.

Iterative Methods for Linear and Nonlinear Equations

Iterative Methods for Linear and Nonlinear Equations PDF

Author: C. T. Kelley

Publisher: SIAM

Published: 1995-01-01

Total Pages: 179

ISBN-13: 9781611970944

DOWNLOAD EBOOK →

Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

Iterative Methods for Solving Nonlinear Equations and Systems

Iterative Methods for Solving Nonlinear Equations and Systems PDF

Author: Juan R. Torregrosa

Publisher: MDPI

Published: 2019-12-06

Total Pages: 494

ISBN-13: 3039219405

DOWNLOAD EBOOK →

Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Nonlinear Symmetries and Nonlinear Equations

Nonlinear Symmetries and Nonlinear Equations PDF

Author: G. Gaeta

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 275

ISBN-13: 9401110182

DOWNLOAD EBOOK →

The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun damental elementary particles physics is actually (physical interpretation of) group theory -the application of symmetry methods to dift"erential equations remained a sleeping beauty for many, many years. The main reason for this lies probably in a fact that is quite clear to any beginner in the field. Namely, the formidable comple:rity ofthe (algebraic, not numerical!) computations involved in Lie method. I think this does not account completely for this oblivion: in other fields of Physics very hard analytical computations have been worked through; anyway, one easily understands that systems of dOlens of coupled PDEs do not seem very attractive, nor a very practical computational tool.

Methods for Solving Systems of Nonlinear Equations

Methods for Solving Systems of Nonlinear Equations PDF

Author: Werner C. Rheinboldt

Publisher: SIAM

Published: 1998-01-01

Total Pages: 157

ISBN-13: 9781611970012

DOWNLOAD EBOOK →

This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.

Nonlinear Differential Equations

Nonlinear Differential Equations PDF

Author: Raimond A. Struble

Publisher: Courier Dover Publications

Published: 2018-01-16

Total Pages: 289

ISBN-13: 0486817547

DOWNLOAD EBOOK →

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.

Nonlinear Wave Equations

Nonlinear Wave Equations PDF

Author: Walter A. Strauss

Publisher: American Mathematical Soc.

Published: 1990-01-12

Total Pages: 106

ISBN-13: 0821807250

DOWNLOAD EBOOK →

The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Lanterna Rally - Theme by Grace Themes