用数值方法求线性常微分方程的超指数解
Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation
摘要：
提出了一种计算多项式系数常线性微分方程超指数解的新算法。该算法依赖于解释正式的系列解决方案在奇点解析函数和评估他们在一些共同的普通点。数值数据被用来确定可能产生超指数解的形式系列的少量组合。
英文摘要：
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic functions and evaluating them numerically at some common ordinary point. The numerical data is used to determine a small number of combinations of the formal series that may give rise to hyperexponential solutions.
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