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A Unified Approach To Boundary Value Problems
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Book Synopsis A Unified Approach to Boundary Value Problems by : Athanassios S. Fokas
Download or read book A Unified Approach to Boundary Value Problems written by Athanassios S. Fokas and published by SIAM. This book was released on 2008-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Book Synopsis Unified Transform for Boundary Value Problems by : Athanasios S. Fokas
Download or read book Unified Transform for Boundary Value Problems written by Athanasios S. Fokas and published by SIAM. This book was released on 2015-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs. The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Book Synopsis Dynamics of Structure and Foundation - A Unified Approach by : Indrajit Chowdhury
Download or read book Dynamics of Structure and Foundation - A Unified Approach written by Indrajit Chowdhury and published by CRC Press. This book was released on 2008-12-17 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to provide engineers with quick access to current and practical information on the dynamics of structure and foundation, this unique work, consisting of two separately available volumes, serves as a complete reference, especially for those involved with earthquake or dynamic analysis, or the design of machine foundations in the oil, gas, a
Book Synopsis Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications by : Fethi Belgacem
Download or read book Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications written by Fethi Belgacem and published by CRC Press. This book was released on 1997-05-05 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic Boundary Value Problems With Indefinite Weights presents a unified approach to the methodologies dealing with eigenvalue problems involving indefinite weights. The principal eigenvalue for such problems is characterized for various boundary conditions. Such characterizations are used, in particular, to formulate criteria for the persistence and extinctions of populations, and applications of the formulations obtained can be quite extensive.
Book Synopsis Initial Boundary Value Problems in Mathematical Physics by : Rolf Leis
Download or read book Initial Boundary Value Problems in Mathematical Physics written by Rolf Leis and published by Courier Corporation. This book was released on 2013-07-17 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to classical scattering theory and time-dependent theory of linear equations in mathematical physics. Topics include wave operators, exterior boundary value problems, radiation conditions, limiting absorption principles, and more. 1986 edition.
Book Synopsis Mathematical Physics II by : Enrico De Micheli
Download or read book Mathematical Physics II written by Enrico De Micheli and published by MDPI. This book was released on 2020-12-15 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The charm of Mathematical Physics resides in the conceptual difficulty of understanding why the language of Mathematics is so appropriate to formulate the laws of Physics and to make precise predictions. Citing Eugene Wigner, this “unreasonable appropriateness of Mathematics in the Natural Sciences” emerged soon at the beginning of the scientific thought and was splendidly depicted by the words of Galileo: “The grand book, the Universe, is written in the language of Mathematics.” In this marriage, what Bertrand Russell called the supreme beauty, cold and austere, of Mathematics complements the supreme beauty, warm and engaging, of Physics. This book, which consists of nine articles, gives a flavor of these beauties and covers an ample range of mathematical subjects that play a relevant role in the study of physics and engineering. This range includes the study of free probability measures associated with p-adic number fields, non-commutative measures of quantum discord, non-linear Schrödinger equation analysis, spectral operators related to holomorphic extensions of series expansions, Gibbs phenomenon, deformed wave equation analysis, and optimization methods in the numerical study of material properties.
Book Synopsis Proceedings of International Scientific Conference on Telecommunications, Computing and Control by : Nikita Voinov
Download or read book Proceedings of International Scientific Conference on Telecommunications, Computing and Control written by Nikita Voinov and published by Springer Nature. This book was released on 2021-04-28 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a platform for academics and practitioners for sharing innovative results, approaches, developments, and research projects in computer science and information technology, focusing on the latest challenges in advanced computing and solutions introducing mathematical and engineering approaches. The book presents discussions in the area of advances and challenges of modern computer science, including telecommunications and signal processing, machine learning and artificial intelligence, intelligent control systems, modeling and simulation, data science and big data, data visualization and graphics systems, distributed, cloud and high-performance computing, and software engineering. The papers included are presented at TELECCON 2019 organized by Peter the Great St. Petersburg University during November 18–19, 2019.
Book Synopsis Evolutionary Equations by : Christian Seifert
Download or read book Evolutionary Equations written by Christian Seifert and published by Springer Nature. This book was released on 2022 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
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.
Book Synopsis Avatar-Based Control, Estimation, Communications, and Development of Neuron Multi-Functional Technology Platforms by : Mkrttchian, Vardan
Download or read book Avatar-Based Control, Estimation, Communications, and Development of Neuron Multi-Functional Technology Platforms written by Mkrttchian, Vardan and published by IGI Global. This book was released on 2019-12-27 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Competition in today’s global market offers strong motivation for the development of sophisticated tools within computer science. The neuron multi-functional technology platform is a developing field of study that regards the various interactive approaches that can be applied within this subject matter. As advancing technologies continue to emerge, managers and researchers need a compilation of research that discusses the advancements and specific implementations of these intelligent approaches with this platform. Avatar-Based Control, Estimation, Communications, and Development of Neuron Multi-Functional Technology Platforms is a pivotal reference source that provides vital research on the application of artificial and natural approaches towards neuron-based programs. While highlighting topics such as natural intelligence, neurolinguistics, and smart data storage, this publication presents techniques, case studies, and methodologies that combine the use of intelligent artificial and natural approaches with optimization techniques for facing problems and combines many types of hardware and software with a variety of communication technologies to enable the development of innovative applications. This book is ideally designed for researchers, practitioners, scientists, field experts, professors, and students seeking current research on the optimization of avatar-based advancements in multifaceted technology systems.
Book Synopsis Chaos, Fractals and Complexity by : Tassos Bountis
Download or read book Chaos, Fractals and Complexity written by Tassos Bountis and published by Springer Nature. This book was released on 2023-10-23 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings contains research results within the framework of the fields of Chaos, Fractals and Complexity, written by experienced professors, young researchers, and applied scientists. It includes reviews of the fields, which are presented in an educational way for the widest possible audience, analytical results, computer simulations and experimental evidence, focusing on mathematical modelling. The papers presented here are selected from lectures given at the 28th Summer School “Dynamical Systems and Complexity”, July 18 – 27, 2022. Topics cover applications of complex systems in Neuroscience, Biology, Photonics, Seismology, Meteorology, and more broadly Physical and Engineering systems. The summer school has a long history, which began at the University of Patras in 1987 and continues with great success to this day. The original main purpose was to introduce young students and researchers of Greece to a new science that emerged several decades ago and continues to grow internationally at an ever increasing rate around the world.
Book Synopsis Numerical Methods for Two-point Boundary-value Problems by : Herbert Bishop Keller
Download or read book Numerical Methods for Two-point Boundary-value Problems written by Herbert Bishop Keller and published by . This book was released on 1968 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Green's Functions and Boundary Value Problems by : Ivar Stakgold
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.
Book Synopsis Elementary Differential Equations with Boundary Value Problems by : William F. Trench
Download or read book Elementary Differential Equations with Boundary Value Problems written by William F. Trench and published by Thomson Brooks/Cole. This book was released on 2001 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Book Synopsis Partial Differential Equations by : Rainer H. Picard
Download or read book Partial Differential Equations written by Rainer H. Picard and published by Walter de Gruyter. This book was released on 2011 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space (rather than an apparently more general Banach space) setting is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations which consider either specific types of partial differential equations or apply a collection of tools for solving a variety of partial differential equations, this book takes a more global point of view by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented. The book aims to be a largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics.
Book Synopsis Numerical Approximation Methods for Elliptic Boundary Value Problems by : Olaf Steinbach
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
