Numerical Approach to Painlevé Transcendents on Unbounded Domains
Numerical Approach to Painlevé Transcendents on Unbounded Domains
复制标题
无界域上 Painlevé 超越数的数值方法
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
N. Stoilov
中科院分区：
文献类型：
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作者：
C. Klein;N. Stoilov
给出了无界域上Painlev'e超越的多域谱方法。这种方法的目的是研究解决方案确定唯一的，可能发散，渐近系列有效的接近无穷大的部门和近似的解决方案的直线完全位于所述部门内，而不需要评估截断的系列在任何有限点。以Painlev'e I方程的tritronqu'ee解为例说明了该方法的精度。
A multidomain spectral approach for Painlev'e transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a, possibly divergent, asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within said sector without the need of evaluating truncations of the series at any finite point. The accuracy of the method is illustrated for the example of the tritronqu'ee solution to the Painlev'e I equation.