Boundary Value Problems On Time Scales Volume Ii
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Boundary Value Problems On Time Scales Volume Ii
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Author : SVETLIN. GEORGIEV
language : en
Publisher: CRC Press
Release Date : 2021-09-21
Boundary Value Problems On Time Scales Volume Ii written by SVETLIN. GEORGIEV and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with categories.
This book is devoted to the qualitative theory of boundary value problems on time scales. It summarizes the most recent contributions in this area. This book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. The book contains two volumes. Volume I presents boundary value problems for first and second order dynamic equations on time scales and is published by the same publisher. Volume II investigates boundary value problems for three, four and higher order dynamic equations on time scales. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, the theory of dynamic equations is an active area of research. The time scale calculus can be applied to any fields in which dynamic processes are described by discrete or continuous time models. T The calculus of time scales has various applications involving non continuous domains such as certain bug populations, phytoremediation of metals, wound healing, maximization problems in economics and traffic problems. Boundary value problems on time scales has been extensively investigated in simulating processes and the phenomena subject to short-time perturbations during their evolution. The text material of this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques.
Boundary Value Problems On Time Scales Volume I
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Author : Svetlin Georgiev
language : en
Publisher: CRC Press
Release Date : 2021-10-14
Boundary Value Problems On Time Scales Volume I written by Svetlin Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Mathematics categories.
Boundary Value Problems on Time Scales, Volume I is devoted to the qualitative theory of boundary value problems on time scales. Summarizing the most recent contributions in this area, it addresses a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. The text contains two volumes, both published by Chapman & Hall/CRC Press. Volume I presents boundary value problems for first- and second-order dynamic equations on time scales. Volume II investigates boundary value problems for three, four, and higher-order dynamic equations on time scales. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, the theory of dynamic equations is an active area of research. The time-scale calculus can be applied to any field in which dynamic processes are described by discrete or continuous time models. The calculus of time scales has various applications involving noncontinuous domains such as certain bug populations, phytoremediation of metals, wound healing, maximization problems in economics, and traffic problems. Boundary value problems on time scales have been extensively investigated in simulating processes and the phenomena subject to short-time perturbations during their evolution. The material in this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. AUTHORS Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior.
Dynamic Equations On Time Scales
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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Dynamic Equations On Time Scales written by Martin Bohner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems
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Author : John R Graef
language : en
Publisher: World Scientific
Release Date : 2018-09-18
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems written by John R Graef and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Mathematics categories.
The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.
Environmental Systems Volume Ii
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Author : Achim Sydow
language : en
Publisher: EOLSS Publications
Release Date : 2010-09-27
Environmental Systems Volume Ii written by Achim Sydow and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-27 with categories.
Environmental Systems is a component of Encyclopedia of Environmental and Ecological Sciences, Engineering and Technology Resources in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. Environmental Systems is something about data handling, modeling and decision making in the field of environmental systems. It includes related basic knowledge on measurement techniques, modeling techniques and models and their applications for decisions making. Environmental engineering / research are based on measurement techniques and related knowledge of natural and life sciences. Developed mathematical and numerical simulation models are tools and strictly purpose oriented, that means suitable for decision making. The three volumes on Environmental Systems are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.
Advances In Dynamic Equations On Time Scales
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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-06
Advances In Dynamic Equations On Time Scales written by Martin Bohner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-06 with Mathematics categories.
Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.
Handbook Of Differential Equations
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Author : Daniel Zwillinger
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Handbook Of Differential Equations written by Daniel Zwillinger and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.
Handbook Of Fractional Calculus For Engineering And Science
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2022-02-16
Handbook Of Fractional Calculus For Engineering And Science written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-16 with Mathematics categories.
Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
Clean Numerical Simulation
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Author : Shijun Liao
language : en
Publisher: CRC Press
Release Date : 2023-10-25
Clean Numerical Simulation written by Shijun Liao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-25 with Mathematics categories.
This book describes the basic principles of Clean Numerical Simulation (CNS) proposed by the author in 2009, as well as several of its applications. Unlike conventional algorithms, CNS gives in a sufficiently long interval of time a convergent chaotic trajectory whose numerical noise is much lower than the true physical solution, so that one can gain accurately. Thus, CNS provides for the first time an ability to check statistics stability of chaos, leading to a completely new concept of "ultra-chaos," which has both trajectory instability and statistics instability, and thus is of a higher disorder. Notably, it is impossible to repeat experimental results of ultra-chaos even in the statistical sense. However, the reproducibility of physical experiments forms a cornerstone for modern science. Thus, ultra-chaos reveals an incompleteness of the modern science paradigm. In addition, it also reveals statistics stability as a precondition for use of conventional algorithms, including direct numerical simulation (DNS). In Clean Numerical Simulation, several conjectures and open problems are proposed, including a modified fourth Clay millennium problem. Indeed, CNS opens the door for us to enter the "clean" numerical world of chaos and turbulence.
Multiplicative Partial Differential Equations
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Author : Svetlin G. Georgiev
language : en
Publisher: CRC Press
Release Date : 2023-10-30
Multiplicative Partial Differential Equations written by Svetlin G. Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-30 with Mathematics categories.
Multiplicative Partial Differential Equations presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The authors' aim is to present a clear and well-organized treatment of the concepts behind the development of mathematics and solution techniques. The text is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. Features Includes new classification and canonical forms of second-order MPDEs Proposes the latest techniques in solving the multiplicative wave equation such as the method of separation of variables and the energy method Useful in allowing for the basic properties of multiplicative elliptic problems, fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, meant-value formulas, strong principle of maximum, multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, and theorems of Liouville and Harnack