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The symbolic computation of series solutions to ordinary differential equations using trees (extended abstract)

机译：使用树的常微分方程的级数解的符号计算（扩展抽象）

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摘要

Algorithms previously developed by the author give formulas which can be used for the efficient symbolic computation of series expansions to solutions of nonlinear systems of ordinary differential equations. As a by product of this analysis, formulas are derived which relate to trees to the coefficients of the series expansions, similar to the work of Leroux and Viennot, and Lamnabhi, Leroux and Viennot.

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作者
Grossman, Robert;
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年度 1991
页码 1-14
总页数 14
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
ALGORITHMS; DIFFERENTIAL EQUATIONS; SERIES EXPANSION; TREES (MATHEMATICS); VECTOR SPACES; COEFFICIENTS; FUNCTIONS (MATHEMATICS); ITERATIVE SOLUTION; LIE GROUPS; NONLINEAR SYSTEMS; RUNGE-KUTTA METHOD;

机译：算法;微分方程;系列扩展;树木（数学）;矢量空间;系数;功能（数学）;迭代解决方案; LIE GROUps;非线性系统; RUNGE-KUTTa方法;

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1. Symbolic Solution of Nonhomogeneous Linear Ordinary Differential Equations in Terms of Power Series [J] . A. A. Ryabenko Programming and Computer Software . 2006,第2期

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2. A symbolic algorithm for exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients near an ordinary point [J] . Kiymaz O Applied mathematics and computation . 2006,第2期

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3. Extended proposed algorithm with symbolic computation to construct exact solutions for some nonlinear differential equations [J] . E.M.E. Zayed, Khaled A. Gepreel, M.M. El Horbaty Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2009,第1期

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4. Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for Excluding Oscillations (Extended Abstract) (Invited Talk) [C] . Andreas Weber, Thomas Sturm, Werner M. Seiler, Computer algebra in scientific computing . 2010

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5. Power series solutions of fractional differential equations and symbolic derivatives and integrals. [D] . Benghorbal, Mhenni M. 2004

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6. Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations [O] . Gabil M. Amiraliyev, Aysenur Ucar 2013

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7. Symbolic Computation of Local Symmetries of Nonlinear and Linear Partial and Ordinary Differential Equations [O] . Alexei F. Cheviakova 2011

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The symbolic computation of series solutions to ordinary differential equations using trees (extended abstract)

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