## Differential Equations with Symbolic ComputationThis 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 of Hilberts Sixteenth Problem | 1 |

Estimating Limit Cycle Bifurcations from Centers | 23 |

Conditions of Infinity to be an Isochronous Center for a Class of Differential Systems | 37 |

Darboux Integrability and Limit Cycles for a Class of Polynomial Differential Systems | 55 |

TimeReversibility in TwoDimensional Polynomial Systems | 67 |

On Symbolic Computation of the LCE of NDimensional Dynamical Systems | 85 |

Symbolic Computation for Equilibria of Two Dynamic Models | 109 |

Attractive Regions in Power Systems by Singular Perturbation Analysis | 121 |

Algorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations | 201 |

Factoring Partial Differential Systems in Positive Characteristic | 213 |

On the Factorization of Differential Modules | 239 |

Continuous and Discrete Homotopy Operators and the Computation of Conservation Laws | 255 |

Partial and Complete Linearization of PDEs Based on Conservation Laws | 291 |

A Maple Package to Construct the Conservation Laws for Nonlinear Evolution Equations | 307 |

Generalized Differential Resultant Systems of Algebraic ODEs and Differential Elimination Theory | 327 |

On Good Bases of AlgebraicoDifferential Ideals | 343 |

Algebraic Multiplicity and the Poincare Problem | 143 |

Formalizing a Reasoning Strategy in Symbolic Approach to Differential Equations | 159 |

Looking for Periodic Solutions of ODE Systems by the Normal Form Method | 173 |

### Other editions - View all

Differential Equations with Symbolic Computation Dongming Wang,Zhiming Zheng No preview available - 2005 |

### Common terms and phrases

1-dimensional submodules algebraic differential equation algebrico-differential algorithm analytic equalities autoreduced bifurcation center conditions center variety coefficients computer algebra conservation laws conserved density consider constant corresponding critical point cubic systems Darboux Darboux integrable decomposition defined Definition denote derivatives differential module differential polynomials differential resultant dynamical systems Efdr eigenvalues equilibrium Euler operators example finite function given Grobner basis homotopy operator irreducible isochronous center Lemma Liapunov quantities Lienard systems limit cycles linear Lyapunov Math Mathematics Mathematics Subject Classification matrix method monomial non-zero nonlinear normal form obtain order algebraic differential origin parameters partial differential system partial p-curvatures PCLaws PDEs periodic solutions polset polynomial differential systems polynomial set polynomial systems problem Proof quadratic rational general solution rational solutions reduced satisfied singular point slow manifold solving stable manifold submodules Symbolic Computation symmetry Theorem theory transformation tuple uniform in rank variables vector field well-behaved basis Xm+r zero