Symmetry Analysis Of Differential Equations With Mathematica
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Symmetry Analysis Of Differential Equations With Mathematica
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Author : Gerd Baumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Symmetry Analysis Of Differential Equations With Mathematica written by Gerd Baumann 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 2013-11-21 with Mathematics categories.
The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie-in honor of Sophus Lie---carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and en gineering is demonstrated by many examples. The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improve ments and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica.
Introduction To Symmetry Analysis Paperback With Cd Rom
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Author : Brian Cantwell
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-23
Introduction To Symmetry Analysis Paperback With Cd Rom written by Brian Cantwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-23 with Mathematics categories.
An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
New Developments In Functional And Fractional Differential Equations And In Lie Symmetry
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Author : Ioannis P. Stavroulakis
language : en
Publisher: MDPI
Release Date : 2021-09-03
New Developments In Functional And Fractional Differential Equations And In Lie Symmetry written by Ioannis P. Stavroulakis and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Science categories.
Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows: Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis.
Proceedings Of The International Conference On Mathematical Sciences And Statistics 2022 Icmss 2022
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Author : Nadihah Wahi
language : en
Publisher: Springer Nature
Release Date : 2023-02-10
Proceedings Of The International Conference On Mathematical Sciences And Statistics 2022 Icmss 2022 written by Nadihah Wahi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-10 with Mathematics categories.
This is an open access book. The ICMSS2022 is an international conference jointly organised by the Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia together with the Banasthali University, Jaipur, India. This international conference aims to give exposure and to bring together academicians, researchers and industry experts for intellectual growth. The ICMSS2022 serves as a platform for the scientific community members to exchange ideas and approaches, to present research findings, and to discuss current issues and topics related to mathematics, statistics as well as their applications. Objectives: to present the most recent discoveries in mathematics and statistics. to serve as a platform for knowledge and information sharing between experts from industries and academia. to identify and create potential collaboration among participants. The organising committee of ICMSS2022 welcomes all delegates to deliberate over various aspects related to the conference themes and sub-themes.
Symmetry Analysis Of Differential Equations
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Author : Daniel J. Arrigo
language : en
Publisher: John Wiley & Sons
Release Date : 2015-01-20
Symmetry Analysis Of Differential Equations written by Daniel J. Arrigo and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-20 with Mathematics categories.
A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. Symmetry Analysis of Differential Equations: An Introduction also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations.
Asymptotic Methods In Nonlinear Wave Phenomena
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Author : Tommaso Ruggeri
language : en
Publisher: World Scientific
Release Date : 2007
Asymptotic Methods In Nonlinear Wave Phenomena written by Tommaso Ruggeri and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena. Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Methods Of Mathematical Modelling And Computation For Complex Systems
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Author : Jagdev Singh
language : en
Publisher: Springer Nature
Release Date : 2021-08-26
Methods Of Mathematical Modelling And Computation For Complex Systems written by Jagdev Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Technology & Engineering categories.
This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.
Continuous Symmetries And Integrability Of Discrete Equations
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Author : Decio Levi
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-01-23
Continuous Symmetries And Integrability Of Discrete Equations written by Decio Levi and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Mathematics categories.
This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.
Computer Algebra In Scientific Computing Casc 2001
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Author : Viktor G. Ganzha
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computer Algebra In Scientific Computing Casc 2001 written by Viktor G. Ganzha 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 Computers categories.
CASC 2001 continues a tradition ~ started in 1998 ~ of international con ferences on the latest advances in the application of computer algebra systems to the solution of various problems in scientific computing. The three ear (CASs) lier conferences in this sequence, CASC'98, CASC'99, and CASC 2000, were held, Petersburg, Russia, in Munich, Germany, and in Samarkand, respectively, in St. Uzbekistan, and proved to be very successful. We have to thank the program committee, listed overleaf, for a tremendous job in soliciting and providing reviews for the submitted papers. There were more than three reviews per submission on average. The result of this job is reflected in the present volume, which contains revised versions of the accepted papers. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scientific computing. In particular, five papers are devoted to the implementation of the analysis of involutive systems with the aid of CASso The specific examples include new efficient algorithms for the computation of Janet bases for monomial ideals, involutive division, involutive reduction method, etc. A number of papers deal with application of CASs for obtaining and vali dating new exact solutions to initial and boundary value problems for partial differential equations in mathematical physics. Several papers show how CASs can be used to obtain analytic solutions of initial and boundary value problems for ordinary differential equations and for studying their properties.
Crc Handbook Of Lie Group Analysis Of Differential Equations Volume Iii
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Author : Nail H. Ibragimov
language : en
Publisher: CRC Press
Release Date : 2024-11-01
Crc Handbook Of Lie Group Analysis Of Differential Equations Volume Iii written by Nail H. Ibragimov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.