Download or read book An Extension of the Method of Averaging to Partial Differential Equations written by Abdelali Ben Lemlih and published by . This book was released on 1986 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Download or read book On Averaging Methods for Partial Differential Equations written by Ferdinand Verhulst and published by . This book was released on 1999 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Method of Averaging for Differential Equations on an Infinite Interval written by Vladimir Burd and published by CRC Press. This book was released on 2007-03-19 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the me
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Download or read book Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.
Download or read book A Generalized Averaging Method for Linear Differential Equations with Almost Periodic Coefficients written by Thomas J. Coakley and published by . This book was released on 1969 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Systems in Control and Signal Processing 1992 written by L. Dugard and published by Elsevier. This book was released on 2014-06-28 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive Systems remain a very interesting field of theoretical research, extended by methodological studies and an increasing number of applications. The plenary papers, invited sessions and contributed sessions focused on many aspects of adaptive systems, such as systems identification and modelling, adaptive control of nonlinear systems and theoretical issues in adaptive control. Also covered were methodological aspects and applications of adaptive control, intelligent tuning and adaptive signal processing.
Download or read book Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2007-08-18 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book A Stability Technique for Evolution Partial Differential Equations written by Victor A. Galaktionov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.
Download or read book Introduction to Partial Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.
Download or read book Partial Differential Equations and Boundary Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Download or read book Partial Differential Equations written by Samuel Earnshaw and published by . This book was released on 1871 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Partial Differential Equations written by William F. Ames and published by . This book was released on 1970 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Toolbox of Averaging Theorems written by Ferdinand Verhulst and published by Springer Nature. This book was released on 2023-08-23 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε. Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs). In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.
Download or read book Group Explicit Methods for the Numerical Solution of Partial Differential Equations written by David J. Evans and published by CRC Press. This book was released on 1997-05-22 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is no doubt that the new methods will be widely used.
