Download or read book Green s Functions in the Theory of Ordinary Differential Equations written by Alberto Cabada and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.
Download or read book Green s Functions in the Theory of Ordinary Differential Equations written by Alberto Cabada and published by . This book was released on 2013-12-31 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Green s Functions and Linear Differential Equations written by Prem K. Kythe and published by CRC Press. This book was released on 2011-01-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs). The text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary
Download or read book Green s Functions Introductory Theory with Applications written by Gary Francis Roach and published by . This book was released on 1970 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Green s Functions in Science and Engineering written by Michael D. Greenberg and published by Courier Dover Publications. This book was released on 2015-08-19 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to coverage of Green's function, this concise introductory treatment examines boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics. Suitable for undergraduate and graduate students. 1971 edition.
Download or read book Green s Functions with Applications written by Dean G. Duffy and published by CRC Press. This book was released on 2001-05-31 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical applications in physics rather than the practical means of finding Green's functions for applications in engineering and the sciences. Green's
Download or read book Advanced Mathematics for Applications written by Andrea Prosperetti and published by Cambridge University Press. This book was released on 2011-01-06 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.
Download or read book Greens Functions and Linear Differential Equations written by Prem K. Kythe and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Green s Functions written by Yuri A. Melnikov and published by Walter de Gruyter. This book was released on 2012-04-02 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.
Download or read book Green s Functions in Applied Mechanics written by Yu. A. Melnikov and published by Computational Mechanics. This book was released on 1995 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is probably the first attempt to make this special topic in the field of partial differential equations accessible to a large audience. The book contains a description of how to construct Green's functions and matrices for elliptic partial differential equations. A number of applications are also presented showing the computational capability of the Green's functions method, and indicate possible ways to put into practice the results of the present study.
Download or read book Green s Functions written by Yuri A. Melnikov and published by Springer. This book was released on 2017-05-08 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.
Download or read book Green s Functions and Finite Elements written by Friedel Hartmann and published by Springer Science & Business Media. This book was released on 2012-08-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.
Download or read book Green s Functions with Applications written by Dean G. Duffy and published by CRC Press. This book was released on 2015-03-10 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since publication of the first edition over a decade ago, Green’s Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green’s function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green’s function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green’s functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green’s functions, each chapter contains a special section devoted to topics where Green’s functions particularly are useful. For example, in the case of the wave equation, Green’s functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green’s functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green’s Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.
Download or read book Green s Functions and Boundary Value Problems written by Ivar Stakgold and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
Download or read book Differential Equations with Involutions written by Alberto Cabada and published by Springer. This book was released on 2016-01-06 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.
Download or read book Two Point Boundary Value Problems Lower and Upper Solutions written by C. De Coster and published by Elsevier. This book was released on 2006-03-21 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. · Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Download or read book Theory of a Higher Order Sturm Liouville Equation written by Vladimir Kozlov and published by Springer. This book was released on 2006-11-13 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.
