Exact Methods For Nonlinear Pdes
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Exact Methods For Nonlinear Pdes
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Author : Andreĭ Dmitrievich Poli︠a︡nin
language : en
Publisher:
Release Date : 2025
Exact Methods For Nonlinear Pdes written by Andreĭ Dmitrievich Poli︠a︡nin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Mathematics categories.
"The book describes and illustrates how to apply effective analytical methods to obtain exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations. Nonlinear partial differential equations of the second and higher orders, including nonlinear equations of mathematical physics, are commonly encountered in various fields of mathematics, physics, mechanics, chemistry, and biology and in numerous applications. Finding a general solution to these equations is only possible in exceptional cases. Therefore, one usually has to limit themselves to identifying and analyzing particular solutions, which are referred to as exact solutions. A solution is exact if, when substituted into the mathematical equation, it turns the equation into an identity. No approximations or simplifications of the equation are allowed, and no a priori assumptions are used. Exact solutions to equations of mathematical physics greatly enhance our understanding of the qualitative features of many phenomena and processes in various fields of natural science. Simple solutions of linear and nonlinear differential equations are widely used to illustrate theoretical material and various applications in university and college courses on applied mathematics, theoretical physics, fluid dynamics, nonlinear optics, and other disciplines. Exact solutions are also necessary to update and improve relevant sections of computer software for analytical calculations (such as computer algebra systems like Mathematica, Maple, MATLAB, and others). The book includes examples and exercises to help the reader better understand the material and develop practical skills in solving nonlinear differential equations. This book will be helpful for a wide range of researchers, university teachers, and engineers, as well as graduate postgraduate and PhD students"--
Exact Methods For Nonlinear Pdes
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2025-07
Exact Methods For Nonlinear Pdes written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07 with Mathematics categories.
The book describes and illustrates how to apply effective analytical methods to obtain exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations.
Separation Of Variables And Exact Solutions To Nonlinear Pdes
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2021-09-19
Separation Of Variables And Exact Solutions To Nonlinear Pdes written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-19 with Mathematics categories.
Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.
Handbook Of Nonlinear Partial Differential Equations Second Edition
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Handbook Of Nonlinear Partial Differential Equations Second Edition written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.
Delay Ordinary And Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2023-08-28
Delay Ordinary And Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
Delay Ordinary and Partial Differential Equations is devoted to linear and nonlinear ordinary and partial differential equations with constant and variable delay. It considers qualitative features of delay differential equations and formulates typical problem statements. Exact, approximate analytical and numerical methods for solving such equations are described, including the method of steps, methods of integral transformations, method of regular expansion in a small parameter, method of matched asymptotic expansions, iteration-type methods, Adomian decomposition method, collocation method, Galerkin-type projection methods, Euler and Runge-Kutta methods, shooting method, method of lines, finite-difference methods for PDEs, methods of generalized and functional separation of variables, method of functional constraints, method of generating equations, and more. The presentation of the theoretical material is accompanied by examples of the practical application of methods to obtain the desired solutions. Exact solutions are constructed for many nonlinear delay reaction-diffusion and wave-type PDEs that depend on one or more arbitrary functions. A review is given of the most common mathematical models with delay used in population theory, biology, medicine, economics, and other applications. The book contains much new material previously unpublished in monographs. It is intended for a broad audience of scientists, university professors, and graduate and postgraduate students specializing in applied and computational mathematics, mathematical physics, mechanics, control theory, biology, medicine, chemical technology, ecology, economics, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on applied mathematics, mathematical physics, and differential equations for delivering special courses and for practical training.
New Numerical And Analytical Methods For Nonlinear Partial Differential Equations With Applications In Quantum Physics
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Author : Mustafa Inc
language : en
Publisher: Frontiers Media SA
Release Date : 2023-11-20
New Numerical And Analytical Methods For Nonlinear Partial Differential Equations With Applications In Quantum Physics written by Mustafa Inc and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Science categories.
Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws
Analytical Techniques For Solving Nonlinear Partial Differential Equations
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Author : Daniel J. Arrigo
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Analytical Techniques For Solving Nonlinear Partial Differential Equations written by Daniel J. Arrigo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, the reader is introduced to techniques used to obtain exact solutions of NPDEs. The chapters include the following topics: Compatibility, Differential Substitutions, Point and Contact Transformations, First Integrals, and Functional Separability. The reader is guided through these chapters and is provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for a second course in PDEs (typically found in both science and engineering programs) and has been used at the University of Central Arkansas for more than ten years.
Proceedings Of The Eighth International Conference On Bio Inspired Computing Theories And Applications Bic Ta 2013
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Author : Zhixiang Yin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-22
Proceedings Of The Eighth International Conference On Bio Inspired Computing Theories And Applications Bic Ta 2013 written by Zhixiang Yin 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 2013-10-22 with Computers categories.
International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA) is one of the flagship conferences on Bio-Computing, bringing together the world’s leading scientists from different areas of Natural Computing. Since 2006, the conferences have taken place at Wuhan (2006), Zhengzhou (2007), Adelaide (2008), Beijing (2009), Liverpool & Changsha (2010), Malaysia (2011) and India (2012). Following the successes of previous events, the 8th conference is organized and hosted by Anhui University of Science and Technology in China. This conference aims to provide a high-level international forum that researchers with different backgrounds and who are working in the related areas can use to present their latest results and exchange ideas. Additionally, the growing trend in Emergent Systems has resulted in the inclusion of two other closely related fields in the BIC-TA 2013 event, namely Complex Systems and Computational Neuroscience. These proceedings are intended for researchers in the fields of Membrane Computing, Evolutionary Computing and Genetic Algorithms, DNA and Molecular Computing, Biological Computing, Swarm Intelligence, Autonomy-Oriented Computing, Cellular and Molecular Automata, Complex Systems, etc. Professor Zhixiang Yin is the Dean of the School of Science, Anhui University of Science & Technology, China. Professor Linqiang Pan is the head of the research group of Natural Computing at Huazhong University of Science and Technology, Wuhan, China. Professor Xianwen Fang also works at the Anhui University of Science & Technology.
Differential Equations
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Author : Dr. Mahadev Biradar
language : en
Publisher: Shineeks Publishers
Release Date : 2024-10-15
Differential Equations written by Dr. Mahadev Biradar and has been published by Shineeks Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-15 with Education categories.
Differential Equations: Methods & Applications offers a comprehensive exploration of differential equations, essential tools for modeling dynamic systems in science and engineering. The book begins with foundational concepts and definitions, progressing through various techniques for solving first-order and second-order linear differential equations, including methods such as Laplace transforms and systems of differential equations. Numerical methods are also highlighted, alongside partial differential equations, emphasizing their applications in physics and engineering. The book concludes with discussions on advanced topics like boundary value problems and Sturm-Liouville theory. Designed for students and professionals, this text combines theory and practical applications, equipping readers with the necessary skills to tackle real-world problems involving differential equations.
Water In Biomechanical And Related Systems
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Author : Adam Gadomski
language : en
Publisher: Springer Nature
Release Date : 2021-04-21
Water In Biomechanical And Related Systems written by Adam Gadomski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-21 with Science categories.
The contributed volume puts emphasis on a superior role of water in (bio)systems exposed to a mechanical stimulus. It is well known that water plays an extraordinary role in our life. It feeds mammalian or other organism after distributing over its whole volume to support certain physiological and locomotive (friction-adhesion) processes to mention but two of them, both of extreme relevance. Water content, not only in the mammalian organism but also in other biosystems such as whether those of soil which is equipped with microbiome or the ones pertinent to plants, having their own natural network of water vessels, is always subjected to a force field.The decisive force field applied to the biosystems makes them biomechanically agitated irrespective of whether they are subjected to external or internal force-field conditions. It ought to be noted that the decisive mechanical factor shows up in a close relation with the space-and-time scale in which it is causing certain specific phenomena to occur.The scale problem, emphasizing the range of action of gravitational force, thus the millimeter or bigger force vs. distance scale, is supposed to enter the so-called macroscale approach to water transportation through soil or plants’ roots system. It is merely related to a percolation problem, which assumes to properly inspect the random network architecture assigned to the biosystems invoked. The capillarity conditions turn out to be of prior importance, and the porous-medium effect has to be treated, and solved in a fairly approximate way.The deeper the scale is penetrated by a force-exerting and hydrated agent the more non-gravitational force fields manifest. This can be envisaged in terms of the corresponding thermodynamic (non-Newtonian) forces, and the phenomena of interest are mostly attributed to suitable changes of the osmotic pressure. In low Reynolds number conditions, thus in the (sub)micrometer distance-scale zone, they are related with the corresponding viscosity changes of the aqueous, e.g. cytoplasmatic solutions, of semi-diluted and concentrated (but also electrolytic) characteristics. For example, they can be observed in articulating systems of mammals, in their skin, and to some extent, in other living beings, such as lizards, geckos or even insects. Through their articulating devices an external mechanical stimulus is transmitted from macro- to nanoscale, wherein the corresponding osmotic-pressure conditions apply. The content of the proposed work can be distributed twofold. First, the biomechanical mammalian-type (or, similar) systems with extraordinary relevance of water for their functioning will be presented, also including a presentation of water itself as a key physicochemical system/medium. Second, the suitably chosen related systems, mainly of soil and plant addressing provenience, will be examined thoroughly. As a common denominator of all of them, it is proposed to look at their hydrophobic and/or (de)hydration effects, and how do they impact on their basic mechanical (and related, such as chemo-mechanical or piezoelectric, etc.) properties. An additional tacit assumption employed throughout the monograph concerns statistical scalability of the presented biosystems which is equivalent to take for granted a certain similarity between local and global system’s properties, mostly those of mechanical nature. The presented work’s chapters also focus on biodiversity and ecological aspects in the world of animals and plants, and the related systems. The chapters’ contents underscore the bioinspiration as the key landmark of the proposed monograph.