Symmetry Analysis Of Differential Equations With Mathematica

Author : Gerd Baumann
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 52,5 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461221104

Get Book

Symmetry Analysis of Differential Equations with Mathematica® by Gerd Baumann Pdf

The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

Author : Brian J. Cantwell
Publisher : Cambridge University Press
Page : 670 pages
File Size : 48,6 Mb
Release : 2002-09-23
Category : Mathematics
ISBN : 1139431714

Get Book

Introduction to Symmetry Analysis by Brian J. Cantwell Pdf

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

Author : Daniel J. Arrigo
Publisher : John Wiley & Sons
Page : 190 pages
File Size : 54,7 Mb
Release : 2015-01-20
Category : Mathematics
ISBN : 9781118721407

Get Book

Symmetry Analysis of Differential Equations by Daniel J. Arrigo Pdf

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.

Author : Mir Sajjad Hashemi,Dumitru Baleanu
Publisher : CRC Press
Page : 208 pages
File Size : 42,8 Mb
Release : 2020-06
Category : Mathematics
ISBN : 1003008550

Get Book

Lie Symmetry Analysis of Fractional Differential Equations by Mir Sajjad Hashemi,Dumitru Baleanu Pdf

"The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here"--

Author : Ioannis P. Stavroulakis,Hossein Jafari
Publisher : MDPI
Page : 156 pages
File Size : 51,6 Mb
Release : 2021-09-03
Category : Science
ISBN : 9783036511580

Get Book

New developments in Functional and Fractional Differential Equations and in Lie Symmetry by Ioannis P. Stavroulakis,Hossein Jafari Pdf

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.

Author : Brian J. Cantwell
Publisher : Cambridge University Press
Page : 655 pages
File Size : 51,6 Mb
Release : 2002-09-26
Category : Mathematics
ISBN : 9781009074452

Get Book

Introduction to Symmetry Analysis by Brian J. Cantwell Pdf

Author : Nail H. Ibragimov
Publisher : CRC Press
Page : 572 pages
File Size : 43,9 Mb
Release : 1995-10-24
Category : Mathematics
ISBN : 0849394198

Get Book

CRC Handbook of Lie Group Analysis of Differential Equations by Nail H. Ibragimov Pdf

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.

Author : George Bluman,Stephen Anco
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 51,8 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387216492

Get Book

Symmetry and Integration Methods for Differential Equations by George Bluman,Stephen Anco Pdf

This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.

Author : Nail H. Ibragimov
Publisher : CRC Press
Page : 452 pages
File Size : 55,8 Mb
Release : 1993-10-20
Category : Mathematics
ISBN : 0849344883

Get Book

CRC Handbook of Lie Group Analysis of Differential Equations by Nail H. Ibragimov Pdf

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 the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

Author : Hans Stephani
Publisher : Cambridge University Press
Page : 278 pages
File Size : 43,5 Mb
Release : 1989
Category : Mathematics
ISBN : 0521366895

Get Book

Differential Equations by Hans Stephani Pdf

This book provides an introduction to the theory and application of the solution of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The theory and application of such methods have therefore attracted increasing attention in the last two decades. In this text the emphasis is on how to find and use the symmetries in different cases. Many examples are discussed, and the book includes more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book an invaluable reference.

Author : Inna Shingareva,Carlos Lizárraga-Celaya
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 47,5 Mb
Release : 2011-07-24
Category : Mathematics
ISBN : 9783709105177

Get Book

Solving Nonlinear Partial Differential Equations with Maple and Mathematica by Inna Shingareva,Carlos Lizárraga-Celaya Pdf

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

Author : Tommaso Ruggeri,Antonio M. Greco,Marco Sammartino
Publisher : World Scientific
Page : 228 pages
File Size : 49,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812708908

Get Book

Asymptotic Methods in Nonlinear Wave Phenomena by Tommaso Ruggeri,Antonio M. Greco,Marco Sammartino Pdf

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.

Author : Debasis Giri,Kim-Kwang Raymond Choo,Saminathan Ponnusamy,Weizhi Meng,Sedat Akleylek,Santi Prasad Maity
Publisher : Springer Nature
Page : 1109 pages
File Size : 49,8 Mb
Release : 2022-03-05
Category : Technology & Engineering
ISBN : 9789811668906

Get Book

Proceedings of the Seventh International Conference on Mathematics and Computing by Debasis Giri,Kim-Kwang Raymond Choo,Saminathan Ponnusamy,Weizhi Meng,Sedat Akleylek,Santi Prasad Maity Pdf

This book features selected papers from the 7th International Conference on Mathematics and Computing (ICMC 2021), organized by Indian Institute of Engineering Science and Technology (IIEST), Shibpur, India, during March 2021. It covers recent advances in the field of mathematics, statistics, and scientific computing. The book presents innovative work by leading academics, researchers, and experts from industry.

Author : George W. Bluman,Sukeyuki Kumei
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 53,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475743074

Get Book

Symmetries and Differential Equations by George W. Bluman,Sukeyuki Kumei Pdf

A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.

Author : Viktor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642566660

Get Book

Computer Algebra in Scientific Computing CASC 2001 by Viktor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf

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.