Nonlinear Equations

Author : C. T. Kelley
Publisher : SIAM
ISBN 13 : 9780898718898
Total Pages : 117 pages
Book Rating : 4.99/5 ( download)

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Download or read book Solving Nonlinear Equations with Newton's Method written by C. T. Kelley and published by SIAM. This book was released on 2003-01-01 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : C. T. Kelley
Publisher : SIAM
ISBN 13 : 9781611970944
Total Pages : 179 pages
Book Rating : 4.46/5 ( download)

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Download or read book Iterative Methods for Linear and Nonlinear Equations written by C. T. Kelley and published by SIAM. This book was released on 1995-01-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniela Lupo
Publisher : Springer Science & Business Media
ISBN 13 : 9783764303983
Total Pages : 284 pages
Book Rating : 4.80/5 ( download)

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Download or read book Nonlinear Equations: Methods, Models and Applications written by Daniela Lupo and published by Springer Science & Business Media. This book was released on 2003-09-25 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : G. Gaeta
Publisher : Springer Science & Business Media
ISBN 13 : 9401110182
Total Pages : 275 pages
Book Rating : 4.81/5 ( download)

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Download or read book Nonlinear Symmetries and Nonlinear Equations written by G. Gaeta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Harold Thayer Davis
Publisher :
ISBN 13 :
Total Pages : 590 pages
Book Rating : 4.0I/5 ( download)

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Download or read book Introduction to Nonlinear Differential and Integral Equations written by Harold Thayer Davis and published by . This book was released on 1960 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Juan R. Torregrosa
Publisher : MDPI
ISBN 13 : 3039219405
Total Pages : 494 pages
Book Rating : 4.07/5 ( download)

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Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Luis A. Caffarelli
Publisher : American Mathematical Soc.
ISBN 13 : 0821804375
Total Pages : 114 pages
Book Rating : 4.77/5 ( download)

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Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

Author : Walter A. Strauss
Publisher : American Mathematical Soc.
ISBN 13 : 0821807250
Total Pages : 106 pages
Book Rating : 4.55/5 ( download)

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Download or read book Nonlinear Wave Equations written by Walter A. Strauss and published by American Mathematical Soc.. This book was released on 1990-01-12 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Raimond A. Struble
Publisher : Courier Dover Publications
ISBN 13 : 0486817547
Total Pages : 289 pages
Book Rating : 4.45/5 ( download)

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Download or read book Nonlinear Differential Equations written by Raimond A. Struble and published by Courier Dover Publications. This book was released on 2018-01-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Valeri? Valer?evich Dolotin
Publisher : World Scientific
ISBN 13 : 9812708006
Total Pages : 286 pages
Book Rating : 4.07/5 ( download)

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Download or read book Introduction to Non-linear Algebra written by Valeri? Valer?evich Dolotin and published by World Scientific. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literaturverz. S. 267 - 269