Modern Nonlinear Equations

Modern Nonlinear Equations
Author: Thomas L. Saaty
Publisher: Courier Corporation
Total Pages: 500
Release: 2012-04-26
Genre: Mathematics
ISBN: 0486143767

Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." — Math Reviews. 1964 edition.

Computational Solution of Nonlinear Systems of Equations

Computational Solution of Nonlinear Systems of Equations
Author: Eugene L. Allgower
Publisher: American Mathematical Soc.
Total Pages: 788
Release: 1990-04-03
Genre: Mathematics
ISBN: 9780821896945

Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Solving Nonlinear Equations with Newton's Method

Solving Nonlinear Equations with Newton's Method
Author: C. T. Kelley
Publisher: SIAM
Total Pages: 117
Release: 2003-01-01
Genre: Mathematics
ISBN: 9780898718898

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.

Lobachevsky Geometry and Modern Nonlinear Problems

Lobachevsky Geometry and Modern Nonlinear Problems
Author: Andrey Popov
Publisher: Springer
Total Pages: 315
Release: 2014-08-06
Genre: Mathematics
ISBN: 3319056697

This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed. The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry.

Nonlinear Partial Differential Equations with Applications

Nonlinear Partial Differential Equations with Applications
Author: Tomás Roubicek
Publisher: Springer Science & Business Media
Total Pages: 415
Release: 2006-01-17
Genre: Mathematics
ISBN: 3764373970

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.

Nonlinear Dispersive Equations

Nonlinear Dispersive Equations
Author: Terence Tao
Publisher: American Mathematical Soc.
Total Pages: 394
Release: 2006
Genre: Mathematics
ISBN: 0821841432

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Partial Differential Equations III

Partial Differential Equations III
Author: Michael E. Taylor
Publisher: Springer Science & Business Media
Total Pages: 734
Release: 2010-11-02
Genre: Mathematics
ISBN: 1441970495

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis

Numerical Methods for Nonlinear Partial Differential Equations

Numerical Methods for Nonlinear Partial Differential Equations
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.

Nonlinear Partial Differential Equations

Nonlinear Partial Differential Equations
Author: Mi-Ho Giga
Publisher: Springer Science & Business Media
Total Pages: 307
Release: 2010-05-30
Genre: Mathematics
ISBN: 0817646515

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.