Formal And Analytic Solutions Of Differential And Difference Equations
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Formal And Analytic Solutions Of Differential And Difference Equations
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Author : Werner Balser
language : en
Publisher:
Release Date : 2012
Formal And Analytic Solutions Of Differential And Difference Equations written by Werner Balser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Difference equations categories.
Formal And Analytic Solutions Of Differential Equations
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Author : Galina Filipuk
language : en
Publisher: World Scientific
Release Date : 2022-03-03
Formal And Analytic Solutions Of Differential Equations written by Galina Filipuk and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Mathematics categories.
The book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.
Complex Differential And Difference Equations
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Author : Galina Filipuk
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-11-18
Complex Differential And Difference Equations written by Galina Filipuk and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-18 with Mathematics categories.
With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.
Formal And Analytic Solutions Of Diff Equations
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Author : Galina Filipuk
language : en
Publisher: Springer
Release Date : 2018-09-24
Formal And Analytic Solutions Of Diff Equations written by Galina Filipuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Mathematics categories.
These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.
Analytic Algebraic And Geometric Aspects Of Differential Equations
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Author : Galina Filipuk
language : en
Publisher: Birkhäuser
Release Date : 2017-06-23
Analytic Algebraic And Geometric Aspects Of Differential Equations written by Galina Filipuk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-23 with Mathematics categories.
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
Differential Difference Equations
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Author : Richard Bellman
language : en
Publisher:
Release Date : 1963
Differential Difference Equations written by Richard Bellman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematics categories.
Advances In Differential And Difference Equations With Applications 2020
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Author : Dumitru Baleanu
language : en
Publisher: MDPI
Release Date : 2021-01-20
Advances In Differential And Difference Equations With Applications 2020 written by Dumitru Baleanu and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Computers categories.
It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.
Formal Analysis
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Author : Xiao-Xiong Gan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-06-08
Formal Analysis written by Xiao-Xiong Gan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Mathematics categories.
Formal analysis is the study of formal power series, formal Laurent series, formal root series, and other formal series or formal functionals. This book is the first comprehensive presentation of the topic that systematically introduces formal analysis, including its algebraic, analytic, and topological structure, along with various applications.
Asymptotic Expansions And Summability
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Author : Pascal Remy
language : en
Publisher: Springer Nature
Release Date : 2024-07-01
Asymptotic Expansions And Summability written by Pascal Remy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.
This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal role in understanding physical, chemical, biological, and ecological phenomena. Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges in this field. The book compares various summability approaches and presents simple applications to PDEs, introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally, it presents moment PDEs, offering a broad class of functional equations including classical, fractional, and q-difference equations. With detailed examples and references, the book caters to readers familiar with the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge, this book provides the necessary tools to understand the complexities of summability theory and its applications to PDEs.
Lectures On Analytic Differential Equations
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Author : I︠U︡. S. Ilʹi︠a︡shenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Analytic Differential Equations written by I︠U︡. S. Ilʹi︠a︡shenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.