A REDUCE package for finding conserved densities of systems of implicit difference–difference equations

Min Gao; Yasuyuki Kato; Masaaki Ito

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A REDUCE package for finding conserved densities of systems of implicit difference–difference equations

机译：一个REDUCE程序包，用于查找隐式差分-差分方程组的守恒密度

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摘要

A computer algebra program for finding polynomial conserved densities of implicit difference–difference equations is presented. The algorithm is based on scaling properties and implemented in computer algebra system REDUCE. The package is applicable to systems of any number of nonlinear difference–difference equations of polynomial type.

机译：提出了一种计算机代数程序，用于查找隐式差分方程的多项式守恒密度。该算法基于缩放属性，并在计算机代数系统REDUCE中实现。该软件包适用于具有多种多项式类型的非线性差分方程的系统。

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《Computer physics communications》 |2004年第1期|共21页
作者
Min Gao; Yasuyuki Kato; Masaaki Ito;
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正文语种 eng
中图分类计算机的应用;
关键词
Conserved density; Implicit difference–difference equation; Computer algebra; REDUCE;

机译：守恒密度;隐式微分方程;计算机代数;REDUCE;

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专利

1. A REDUCE package for finding conserved densities of systems of implicit difference–difference equations [J] . Min Gao, Yasuyuki Kato, Masaaki Ito Computer physics communications . 2004,第1期

机译：一个REDUCE程序包，用于查找隐式差分-差分方程组的守恒密度
2. COMPUTATION OF CONSERVED DENSITIES FOR SYSTEMS OF NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS [J] . Goktas U., Erdmann G., Hereman W. Physics Letters, A . 1997,第1a2期

机译：非线性微分-差分方程组守恒密度的计算
3. Implicit difference methods for infinite systems of hyperbolic functional differential equations [J] . ANNA SZAFRANSKA Annales Societatis Mathematicae Polonae, Seria I. Commentationes mathematicae . 2010,第1期

机译：双曲泛函微分方程无穷系统的隐式差分方法
4. Symbolic Computation of Polynomial Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations [C] . W. Hereman, J. A. Sanders, J. Sayers, Workshop on Group Theory and Numerical Analysis . 2005

机译：非线性差分方程多项式保守密度，广义对称性和递归算子的象征性计算
5. Stability and convergence results for difference approximations of overdetermined differential-algebraic equations with application to implicit integration of constrained mechanical system dynamics. [D] . Lee, Ming-Gong. 1992

机译：超定微分代数方程差分逼近的稳定性和收敛性结果在约束机械系统动力学的隐式积分中的应用。
6. Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions [O] . Vyacheslav A. Trofimov, Evgeny M. Trykin 2012

机译：基于Rosenbrock方法的含人工边界条件的非线性Schrödinger方程的隐式有限差分格式
7. Computation of Conserved Densities for Systems of Nonlinear Differential-Difference Equations [O] . Ünal Goktas, Willy Hereman, Grant Erdmann 1997

机译：非线性微分方程组守恒密度的计算
8. An Investigation of the Method of Finite Elements with Accuracy Comparisons to the Method of Finite Differences for Solution of the Transient Heat Conduction Equation Using Optimum Implicit Formulations. [R] . geneczko,joseph c. 1978

机译：用最优隐式公式求解瞬态热传导方程有限差分法精度有限元法的研究。

A REDUCE package for finding conserved densities of systems of implicit difference–difference equations

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