Differential Equations with Symbolic Computation

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Dongming Wang, Zhiming Zheng
Springer Science & Business Media, Mar 16, 2006 - Mathematics - 374 pages
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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.

 

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Contents

Symbolic Computation of Lyapunov Quantities and the Second Part
1
Estimating Limit Cycle Bifurcations from Centers
23
Conditions of Infinity to be an Isochronous Center for a Class
37
Darboux Integrability and Limit Cycles for a Class of Polynomial
54
On Symbolic Computation of the LCE of NDimensional Dynamical
84
Symbolic Computation for Equilibria of Two Dynamic Models
109
Algebraic Multiplicity and the Poincaré Problem 143 Jinzhi Lei and Lijun Yang
158
Looking for Periodic Solutions of ODE Systems by the Normal Form
173
On the Factorization of Differential Modules
239
Continuous and Discrete Homotopy Operators and the Computation
255
Partial and Complete Linearization of PDEs Based on Conservation
291
A Maple Package to Construct the Conservation Laws
307
Generalized Differential Resultant Systems of Algebraic ODEs
326
On Good Bases of AlgebraicoDifferential Ideals
343
Index
369
Copyright

viii
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