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Differential Equations With Symbolic Computation
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Book Synopsis Differential Equations with Symbolic Computation by : Dongming Wang
Download or read book Differential Equations with Symbolic Computation written by Dongming Wang and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Book Synopsis Algebraic and Symbolic Computation Methods in Dynamical Systems by : Alban Quadrat
Download or read book Algebraic and Symbolic Computation Methods in Dynamical Systems written by Alban Quadrat and published by Springer. This book was released on 2020-04-07 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.
Book Synopsis Computer Algebra and Differential Equations by : E. Tournier
Download or read book Computer Algebra and Differential Equations written by E. Tournier and published by Cambridge University Press. This book was released on 1994-03-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected papers from the Computer Algebra and Differential Equations meeting held in France in June 1992.
Book Synopsis The Symbolic Computation of Integrability Structures for Partial Differential Equations by : Joseph Krasil'shchik
Download or read book The Symbolic Computation of Integrability Structures for Partial Differential Equations written by Joseph Krasil'shchik and published by Springer. This book was released on 2018-04-03 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.
Book Synopsis Differential Equations and Computer Algebra by : Michael F. Singer
Download or read book Differential Equations and Computer Algebra written by Michael F. Singer and published by . This book was released on 1991 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaches computer algebra users about up-to-date research developments in differential equations, with selected papers from CADE 1990, held at Cornell University. Featuring US and European research figures, this book demonstrates scientific computing applications.
Book Synopsis Numerical and Symbolic Scientific Computing by : Ulrich Langer
Download or read book Numerical and Symbolic Scientific Computing written by Ulrich Langer and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.
Book Synopsis Transform Methods for Solving Partial Differential Equations by : Dean G. Duffy
Download or read book Transform Methods for Solving Partial Differential Equations written by Dean G. Duffy and published by CRC Press. This book was released on 2004-07-15 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana
Book Synopsis Algebraic and Symbolic Computation Methods in Dynamical Systems by : Alban Quadrat
Download or read book Algebraic and Symbolic Computation Methods in Dynamical Systems written by Alban Quadrat and published by Springer Nature. This book was released on 2020-05-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.
Book Synopsis Progress in Computing by : Emiliano Grossman
Download or read book Progress in Computing written by Emiliano Grossman and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symbolic Computation by : Robert Grossman
Download or read book Symbolic Computation written by Robert Grossman and published by SIAM. This book was released on 1989-01-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph that describes current research efforts in the application of symbolic computation to several areas, including dynamical systems, differential geometry, Lie algebras, numerical analysis, fluid dynamics, perturbation theory, control theory, and mechanics. The chapters, which illustrate how symbolic computations can be used to study various mathematical structures, are outgrowths of the invited talks that were presented at the NASA-Ames Workshop on The Use of Symbolic Methods to Solve Algebraic and Geometric Problems Arising in Engineering. More than 100 people participated in the two-day conference, which took place in January 1987 at the NASA-Ames Research Center in Moffett Field, California. The field of symbolic computation is becoming increasingly important in science, engineering, and mathematics. The availability of powerful computer algebra systems on workstations has made symbolic computation an important tool for many researchers.
Book Synopsis Numerical and Symbolic Scientific Computing by : Ulrich Langer
Download or read book Numerical and Symbolic Scientific Computing written by Ulrich Langer and published by Springer. This book was released on 2011-11-23 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.
Book Synopsis Computer-Aided Analysis of Difference Schemes for Partial Differential Equations by : Victor G. Ganzha
Download or read book Computer-Aided Analysis of Difference Schemes for Partial Differential Equations written by Victor G. Ganzha and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations * Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary toimplement each algorithm * Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.
Book Synopsis Computational Differential Equations by : Kenneth Eriksson
Download or read book Computational Differential Equations written by Kenneth Eriksson and published by Cambridge University Press. This book was released on 1996-09-05 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Book Synopsis Numerical and Symbolic Computation by : Maria Amélia Ramos Loja
Download or read book Numerical and Symbolic Computation written by Maria Amélia Ramos Loja and published by MDPI. This book was released on 2020-12-29 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive set of articles reflecting on the application of symbolic and/or numerical computation in a range of scientific areas within the fields of engineering and science. These articles constitute extended versions of communications presented at the 4th International Conference on Numerical and Symbolic Computation—SYMCOMP 2019—that took place in Porto, Portugal, from 11 to 12 April 2019 The different chapters present diverse perspectives on the existing effective connections between mathematical methods and procedures and other knowledge areas. The intrinsic multidisciplinary character is visible throughout the whole book as a result of the applicability of the scope and the applications considered. The reader will find this book to be a useful resource for identifying problems of interest in different engineering and science areas, and in the development of mathematical models and procedures used in the context of prediction or verification computational tools as well as in the aided-learning/teaching context. This book is a must-read for anyone interested in the recent developments and applications of symbolic and numerical computation for a number of multidisciplinary engineering and science problems.
Book Synopsis Loewy Decomposition of Linear Differential Equations by : Fritz Schwarz
Download or read book Loewy Decomposition of Linear Differential Equations written by Fritz Schwarz and published by Springer Science & Business Media. This book was released on 2012-09-29 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.
Book Synopsis Computerized Symbolic Manipulation in Mechanics by : Edwin Kreuzer
Download or read book Computerized Symbolic Manipulation in Mechanics written by Edwin Kreuzer and published by Springer. This book was released on 2014-05-04 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present important software tools, basic concepts, methods, and highly sophisticated applications of computerized symbolic manipulation to mechanics problems. An overview about general-purpose symbolic software is followed by general guidelines how to develop and implement high-quality computer algebra code. The theoretical background including modeling techniques for mechanical systems is provided which allows for the computer aided generation of the symbolic equation of motion for multibody systems. It is shown how the governing equations for different types of problems in structural mechanics can be automatically derived and how to implement finite element techniques via computer algebra software. Perturbation methods as a very powerful approach for nonlinear problems are discussed in detail and are demonstrated for a number of applications. The applications covered in this book represent some of the most advanced topics in the rapidly growing field of research on symbolic computation.
Book Synopsis Mathematics for Physical Science and Engineering by : Frank E. Harris
Download or read book Mathematics for Physical Science and Engineering written by Frank E. Harris and published by Academic Press. This book was released on 2014-05-24 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Physical Science and Engineering is a complete text in mathematics for physical science that includes the use of symbolic computation to illustrate the mathematical concepts and enable the solution of a broader range of practical problems. This book enables professionals to connect their knowledge of mathematics to either or both of the symbolic languages Maple and Mathematica. The book begins by introducing the reader to symbolic computation and how it can be applied to solve a broad range of practical problems. Chapters cover topics that include: infinite series; complex numbers and functions; vectors and matrices; vector analysis; tensor analysis; ordinary differential equations; general vector spaces; Fourier series; partial differential equations; complex variable theory; and probability and statistics. Each important concept is clarified to students through the use of a simple example and often an illustration. This book is an ideal reference for upper level undergraduates in physical chemistry, physics, engineering, and advanced/applied mathematics courses. It will also appeal to graduate physicists, engineers and related specialties seeking to address practical problems in physical science. Clarifies each important concept to students through the use of a simple example and often an illustration Provides quick-reference for students through multiple appendices, including an overview of terms in most commonly used applications (Mathematica, Maple) Shows how symbolic computing enables solving a broad range of practical problems
