Modern Group Analysis Advanced Analytical And Computational Methods In Mathematical Physics
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| Author | : N.H. Ibragimov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 379 |
| Release | : 2011-06-27 |
| Genre | : Mathematics |
| ISBN | : 9401120501 |
On the occasion of the 150th anniversary of Sophus Lie, an International Work shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: • classical Lie groups applied for constructing invariant solutions and conservation laws; • conditional (partial) symmetries; • Backlund transformations; • approximate symmetries; • group analysis of finite-difference equations; • problems of group classification; • software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.
| Author | : J Fleischer |
| Publisher | : World Scientific |
| Total Pages | : 370 |
| Release | : 1995-08-31 |
| Genre | : |
| ISBN | : 9814549053 |
Systems and tools of computer algebra (Like AXIOM, Derive, FORM, Mathematica, Maple, Mupad, REDUCE, Macsyma…) let us manipulate extremely complex algebraic formulae symbolically on a computer. Contrary to numerics these computations are exact and there is no loss of accuracy. After decades of research and development, these tools are now becoming as indispensable in Science and Engineering as traditional number crunching already is.The ZiF'94 workshop is amongst the first devoted specifically to applications of computer algebra (CA) in Science and Engineering. The book documents the state of the art in this area and serves as an important reference for future work.
| Author | : Joshua Allensworth Leslie |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821829645 |
This volume contains papers based on some of the talks given at the NSF-CBMS conference on ``The Geometrical Study of Differential Equations'' held at Howard University (Washington, DC). The collected papers present important recent developments in this area, including the treatment of nontransversal group actions in the theory of group invariant solutions of PDEs, a method for obtaining discrete symmetries of differential equations, the establishment of a group-invariant version of the variational complex based on a general moving frame construction, the introduction of a new variational complex for the calculus of difference equations and an original structural investigation of Lie-Backlund transformations. The book opens with a modern and illuminating overview of Lie's line-sphere correspondence and concludes with several interesting open problems arising from symmetry analysis of PDEs. It offers a rich source of inspiration for new or established researchers in the field. This book can serve nicely as a companion volume to a forthcoming book written by the principle speaker at the conference, Professor Niky Kamran, to be published in the AMS series, CBMS Regional Conference Series in Mathematics.
| Author | : Viktor G. Ganzha |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 543 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642566669 |
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.
| Author | : Sergey V. Meleshko |
| Publisher | : Springer |
| Total Pages | : 314 |
| Release | : 2010-06-23 |
| Genre | : Science |
| ISBN | : 9048137977 |
This book provides an accessible yet comprehensive description of the application methods of group analysis to integro-differential equations. It offers both fundamental theoretical and algorithmic aspects of these methods and includes instructive examples.
| Author | : Jörg Volkmann |
| Publisher | : Cuvillier Verlag |
| Total Pages | : 153 |
| Release | : 2007 |
| Genre | : |
| ISBN | : 3867274223 |
| Author | : Nail H. Ibragimov |
| Publisher | : CRC Press |
| Total Pages | : 572 |
| Release | : 1995-10-24 |
| Genre | : Mathematics |
| ISBN | : 9780849394195 |
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 | : Ruffini Remo |
| Publisher | : World Scientific |
| Total Pages | : 2024 |
| Release | : 1997-03-19 |
| Genre | : |
| ISBN | : 9814550000 |
Since 1975, the triennial Marcel Grossmann Meetings have been organized in order to provide opportunities for discussing recent advances in gravitation, general relativity and relativisitic field theories, emphasizing mathematical foundations, physical predictions, and experimental tests.The proceedings of the Seventh Marcel Grossmann Meeting include the invited papers given at the plenary sessions, the summaries of the parallel sessions, the contributed papers presented at the parallel sessions, and the evening public lectures.The authors of these papers discuss many of the recent theoretical, observational, and experimental developments that have significant implications for the fields of physics, cosmology, and relativistic astrophysics.
| Author | : Ronald A. DeVore |
| Publisher | : Cambridge University Press |
| Total Pages | : 418 |
| Release | : 2001-05-17 |
| Genre | : Mathematics |
| ISBN | : 9780521003490 |
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
| Author | : Victor G. Ganzha |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 507 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642602185 |
The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions. CASC'99 is the second conference devoted to applications of computer al gebra in scientific computing. The first conference in this sequence, CASC'98, was held 20-24 April 1998 in St. Petersburg, Russia. This volume contains revised versions of the papers submitted by the par ticipants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scien tific computing: symbolic-numeric analysis and solving differential equations, efficient computations with polynomials, groups, matrices and other related objects, special purpose programming environments, application to physics, mechanics, optics and to other areas. In particular, a significant group of papers deals with applications of com puter algebra methods for the solution of current problems in group theory, which mostly arise in mathematical physics.
