Stokes geometry of higher order ordinary differential equations and middle convolutions
Stokes geometry of higher order ordinary differential equations and middle convolutions
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高阶常微分方程和中间卷积的斯托克斯几何
DOI：
10.1016/j.aim.2017.02.006
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发表时间：
2017
影响因子：
1.7
通讯作者：
T. Motegi and Y. Takei
中科院分区：
文献类型：
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作者：
Atsushi Ichino;Yuji Yoshino;T. Motegi and Y. Takei
中间卷积由Katz引入，由Dettweiler-Reiter、Oshima等人发展，定义了多项式系数线性常微分方程的约简运算。本文利用Aoki-Kawai-Takei提出的精确最陡下降法思想，研究了高阶大参数线性常微分方程经中卷积化约为二阶方程时，如何确定其完全Stokes几何以及如何获得其WKB解的Borel可和性。为了说明该方法的实用性，我们还对一些具体的算例进行了数值研究。
The middle convolution, introduced by Katz and developed by Dettweiler–Reiter, Oshima and others, defines an operation of reduction of linear ordinary differential equations with polynomial coefficients. In this paper, employing an idea of the exact steepest descent method proposed by Aoki–Kawai–Takei, we study how to determine the complete Stokes geometry and how to obtain the Borel summability of WKB solutions of a higher order linear ordinary differential equation with a large parameter when it is reduced to a second order equation via middle convolution. To show the practical usefulness of the method, we also investigate some concrete examples numerically.