Computer Algebra And Differential Equations
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Computer Algebra and Differential Equations
Ordinary differential equations have been studied by mathematicians for many years and the standard techniques have been either by series expansions or by numerical methods. Computer algebra has introduced an alternative means of treating differential equations and solving them more readily.**This volume assembles contributions from leading mathematicians in this growing field of computer algebra.
Involution
Author: Werner M. Seiler
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-10-26
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.