Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models
Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models
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非线性物理模型等价变换和参数约简的符号计算
DOI：
10.1016/j.cpc.2017.06.013
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Cheviakov
中科院分区：
文献类型：
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作者：
A. Cheviakov
利用egemformple软件，对包含任意元素（任意函数和/或任意常数参数）的微分方程组的等价变换李群和广义等价变换的符号计算提供了一个有效的系统程序。讨论了等价变换在给定方程组中任意元素数约简中的应用，并给出了几个例子。给出了广义等价变换的第一个计算实例，其中因变量的变换涉及任意本构函数。作为一个详细的物理例子，考虑了描述不可压缩超弹性纤维增强介质有限反平面剪切位移的三参数非线性波动方程族。计算并采用等效变换从根本上简化了任意纤维方向的模型，将模型可逆地简化为对应于特定纤维方向的简单形式，并且不涉及任意元素。所提出的计算算法适用于包含任意元素的广义微分方程组。
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software packageGeMforMaple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. The first computational example of generalized equivalence transformations where the transformation of the dependent variable involves an arbitrary constitutive function is presented.As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelastic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements.The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements.