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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.
List of contents
Symbolic Computation of Lyapunov Quantities and the Second Part of Hilbert s Sixteenth Problem.- Estimating Limit Cycle Bifurcations from Centers.- Conditions of Infinity to be an Isochronous Center for a Class of Differential Systems.- Darboux Integrability and Limit Cycles for a Class of Polynomial Differential Systems.- Time-Reversibility in Two-Dimensional Polynomial Systems.- On Symbolic Computation of the LCE of N-Dimensional Dynamical Systems.- Symbolic Computation for Equilibria of Two Dynamic Models.- Attractive Regions in Power Systems by Singular Perturbation Analysis.- Algebraic Multiplicity and the Poincaré Problem.- Formalizing a Reasoning Strategy in Symbolic Approach to Differential Equations.- Looking for Periodic Solutions of ODE Systems by the Normal Form Method.- Algorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations.- Factoring Partial Differential Systems in Positive Characteristic.- On the Factorization of Differential Modules.- Continuous and Discrete Homotopy Operators and the Computation of Conservation Laws.- Partial and Complete Linearization of PDEs Based on Conservation Laws.- CONSLAW: A Maple Package to Construct the Conservation Laws for Nonlinear Evolution Equations.- Generalized Differential Resultant Systems of Algebraic ODEs and Differential Elimination Theory.- On Good Bases of Algebraico-Differential Ideals.- On the Construction of Groebner Basis of a Polynomial Ideal Based on Riquier Janet Theory.
Summary
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.
Additional text
From the reviews:
“The book comprises 20 paper-like chapters written by different authors. … the presented topics are well covered by the contributions and since the information content of each chapter is further enhanced by a rich reference section, researchers and students pursuing the relevant subjects should not miss this book.” (Jan Chleboun, Applications of Mathematics, Vol. 56 (5), 2011)
