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.
Inhaltsverzeichnis
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.
