Algebraic Differential Equations
Algebraic Differential Equations
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代数微分方程
DOI：
10.1007/978-3-662-10176-6_6
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
J. Shackell
中科院分区：
文献类型：
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作者：
J. Shackell
渐近论在微分方程组的研究中得到了广泛的应用。待定系数法是一种常用的方法。在最基本的情况下，这包括在方程中代入一个一般的幂函数级数，然后比较项以求出系数。同样的想法也可以用来处理其他基函数中的级数，以及可能出现几个不同基函数的级数，例如plexand logx。缺点是必须事先知道将需要哪些基函数。在这类问题上有大量的专业知识，特别是对于线性常微分方程式；例如，见[119]。在本章中，我们将研究使用嵌套展开可以对非线性方程做些什么。
Asymptotics have been much used in the study of differential equations. The method ofundetermined coefficientsis one common technique. At its most basic, this consists of substituting a general power series into the equation and then comparing terms in order to find the coefficients. The same idea can be made to work with series in other base functions, and also series where several different base functions may appear, for examplexand logxA drawback is that one has to know in advance which base functions are going to be needed. There is a great fund of expertise on such questions, especially for linear ordinary differential equations; see [119] for example. In this chapter, we look at what can be done for non-linear equations using nested expansions.