Download PDF BookApplications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications)

Free Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications)

Free Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications)

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Book Details :
Published on: 2010-12-01
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Original language: English

Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functionals, this book focuses on the preservation of complete symmetry of original differential equations in numerical schemes. This symmetry preservation results in symmetry reduction of the difference model along with that of the original partial differential equations and in order reduction for ordinary difference equations. A substantial part of the book is concerned with conservation laws and first integrals for difference models. The variational approach and Noether type theorems for difference equations are presented in the framework of the Lagrangian and Hamiltonian formalism for difference equations. In addition, the book develops difference mesh geometry based on a symmetry group, because different symmetries are shown to require different geometric mesh structures. The method of finite-difference invariants provides the mesh generating equation, any special case of which guarantees the mesh invariance. A number of examples of invariant meshes is presented. In particular, and with numerous applications in numerics for continuous media, that most evolution PDEs need to be approximated on moving meshes. Based on the developed method of finite-difference invariants, the practical sections of the book present dozens of examples of invariant schemes and meshes for physics and mechanics. In particular, there are new examples of invariant schemes for second-order ODEs, for the linear and nonlinear heat equation with a source, and for well-known equations including Burgers equation, the KdV equation, and the Schrödinger equation. Partial differential equation - Wikipedia In mathematics a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. MATHEMATICS - University of Washington COLLEGE OF ARTS & SCIENCES MATHEMATICS Detailed course offerings (Time Schedule) are available for. Winter Quarter 2017; Spring Quarter 2017; Summer Quarter 2017 NSERC List of Evaluation Groups and Research Topics List of Evaluation Groups and Research Topics. Further to the recommendations from the International Review of Discovery Grants and the Grant Selection Committee (GSC ... RIMS Workshop --- New transformation groups and its ... Theory of Biomathemtics and its Applications - Modeling and Analysis for Discrete and Continuous Models Location Rm 420 Period: 2016-11-14--2016-11-17 Free Differential Equations Books Download Ebooks Online The aim of this book is to give a self contained introduction to the field of ordinary differential equations with emphasis on the dynamical systems point of view ... Discrete mathematics - Wikipedia Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the ... FreeBookCentre - online free computer science ebooks Freebookcentre.net contains links to thousands of free online technical books. Which Include core computer science networking programming languages Systems ... AERONAUTICS & ASTRONAUTICS COLLEGE OF ENGINEERING AERONAUTICS & ASTRONAUTICS Detailed course offerings (Time Schedule) are available for. Winter Quarter 2017; Spring Quarter 2017 The 100 Greatest Mathematicians - fabpedigree.com The Hundred Greatest Mathematicians of the Past. This is the long page with list and biographies. (Click here for just the List with links to the biographies. Mathematics Calendar - American Mathematical Society Mathematics Calendar. Questions and answers regarding this page can be sent to mathcal@ams.org. You can submit an entry to the Mathematics Calendar by filling out ...
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