欠定线性常微分方程的参数解
The Parametric Solution of Underdetermined linear ODEs
摘要：
本文件有两个目的。所提出的算法的一个直接的实际用途是它的适用性欠定线性常微分方程（ODE）的系数是任意的解析函数的自变量的参数解。第二个概念性的目标是提出一种算法，在某种意义上是双重的基本欧几里德算法，因此替代的特殊情况下的Groebner基础算法，因为它是用于解决线性常微分方程系统。本文将欧氏算法与新的对偶算法进行了比较，分析了它们在求解欠定常微分方程问题上的互补性。所描述的算法的实现可以在http://lie.math.brocku.ca/crack/demo下交互地访问。
英文摘要：
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Groebner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new `dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible under http://lie.math.brocku.ca/crack/demo.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
