## Differential Equations with Symbolic ComputationDongming Wang, Zhiming Zheng 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

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 |

369 | |

viii | 201 |

### 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 cubic systems D-modules Darboux Darboux integrable deﬁned Deﬁnition denote derivatives differential modules differential polynomials differential resultant dynamical systems eigenvalues equilibrium Euler operators example ﬁeld finite ﬁrst flux function given Gröbner Gröbner basis homotopy operator irreducible isochronous center Lemma Liapunov quantities limit cycles linear Lyapunov Math Mathematics Mathematics Subject Classification matrix method monomial nonlinear normal form obtain order algebraic differential origin parameters partial differential system partial p-curvatures PDEs periodic solutions polset polynomial ideal polynomial set polynomial systems problem Proof quadratic rational general solution rational solutions reduced satisﬁes singular point stable manifold submodules Symbolic Computation symmetry Theorem theory transformation tuple uniform in rank variables vector field well-behaved basis zero