Algorithmic Lie Theory for Solving Ordinary Differential Equations
Regular price
€248.00
14 days return policy
Shipping & Delivery
A01=Fritz Schwarz
Abel Equation
advanced mathematical physics
algebra
algorithmic symmetry analysis for ODEs
Author_Fritz Schwarz
base
canonical
Canonical Variables
Category=PBF
Category=PBKJ
Category=UB
Category=UY
class
computer algebra systems
continuous symmetry methods
differential invariants
eq_bestseller
eq_computing
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
equivalence
form
galois
Galois Group
group
Infinitesimal Generators
Janet bases theory
Lie Algebra Type
Lie Algebras
Lie Transformation Group
Linear Ode
Linear PDE
Loewy decomposition
Non-constant Solution
Nontrivial Symmetry
Order Equations
Order Ode
Ordinary Differential Equations
Rational Normal Form
Step S2
symmetry
Symmetry Algebra
Symmetry Analysis
Symmetry Class
Symmetry Generator
Symmetry Group
Symmetry Type
Transformation Functions
type
Type L3
Undetermined Functions
Product details
- ISBN 9781584888895
- Weight: 748g
- Dimensions: 156 x 234mm
- Publication Date: 02 Oct 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results.
After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2-D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems.
Schwarz, Fritz
