Abel ODEs: Equivalence and integrable classes

E. S. Cheb-Terrab; A. D. Roche

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Abel ODEs: Equivalence and integrable classes

机译：Abel ODE：等价类和可积类

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A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of the works by Abel (1881), Liouville (1886) and Appell(1889), is also shown. Computer algebra routines were developed to solve ODEs members of these classes by solving their related equivalence problem. The resulting library permits a systematic solving of Abel type ODEs in the Maple symbolic computing environment.

机译：根据不变理论，对非恒定不变的Abel ODE进行了分类，该分类在文献中被称为可解决的。还显示了一组新的可集成类，它们取决于一个或没有一个参数，这些类是根据Abel（1881），Liouville（1886）和Appell（1889）的作品分析得出的。开发了计算机代数例程以通过解决它们的相关等价问题来解决这些类别的ODE成员。生成的库允许在Maple符号计算环境中系统地解决Abel类型的ODE。

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《Computer physics communications》 |2000年第2期|共28页
作者
E. S. Cheb-Terrab; A. D. Roche;
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正文语种 eng
中图分类计算机的应用;
关键词
first order ordinary differential equations of Abel type; equivalence; integrable classes; symbolic computation;

机译：一阶Abel型常微分方程;等价;可积类;符号计算;

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专利

1. Abel ODEs: Equivalence and integrable classes [J] . E. S. Cheb-Terrab, A. D. Roche Computer physics communications . 2000,第1a2期

机译：Abel ODE：等价类和可积类
2. Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations) [J] . Dimitrios E. Panayotounakos, Theodoros I. Zarmpoutis International journal of mathematics and mathematical sciences . 2011,第13期

机译：某些不可解的非线性ODE类（第一类和相对退化方程的Abel非线性ODE）的精确参数或闭式解的构造
3. Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations) [J] . Dimitrios E.Panayotounakos, Theodoros I.Zarmpoutis International journal of mathematics and mathematical sciences . 2011,第2期

机译：构建一些无法解决的非线性非线性杂散的确切参数或闭合形式解决方案（abel的第一类和相对退化等式的非线性杂散）
4. Scaling Up the Greedy Equivalence Search Algorithm by Constraining the Search Space of Equivalence Classes [C] . Juan I. Alonso-Barba, Luis de la Ossa, Jose A. Gamez, Symbolic and quantitative approaches to reasoning with uncertainty . 2011

机译：通过限制等价类的搜索空间来扩大贪婪的等价搜索算法
5. A New Method for Functional Decomposition of Rational Invariants, and the Solution of Abel's Differential Equation via the Equivalence Method. [D] . Roche, Austin Duncan. 2010

机译：有理不变量函数分解的新方法，以及通过等价法求解Abel微分方程的方法。
6. Predicting the extension of equivalence classes from primary generalization gradients: the merger of equivalence classes and perceptual classes. [O] . L Fields, K F Reeve, B J Adams, 1997

机译：从主要泛化梯度预测等价类的扩展：等价类和感知类的合并。
7. Abel ODEs: Equivalence and Integrable Classes [O] . E.S. Cheb-Terrab, A. D. Roche 2007

机译：abel ODEs：等价和可积的类

Abel ODEs: Equivalence and integrable classes

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