论文标题
painlevéII的解决方案实际间隔：新型近似序列
Solutions of Painlevé II on real intervals: novel approximating sequences
论文作者
论文摘要
构建了带有Neumann边界条件的真实线的有限间隔，在PainlevéII的溶液中的新型序列。数值实验强烈表明这些序列在令人惊讶的范围内，甚至普通扰动系列无法收敛的情况。这些序列在这里被标记为非凡的特性。此类序列的每个元素都按其自己的间隔定义。随着序列（显然）收敛到PainlevéII的相应边界值问题的解决方案，这些间隔本身（显然）会收敛到该问题的定义间隔，并且相关常数（显然）（显然）在PainlevéII方程本身中会收敛到常数。每个非凡序列都是以非线性方式构建的，从扰动序列近似到补充边界价值问题的解决方案，涉及电位研究研究中出现的PainlevéII的概括。
Novel sequences of approximants to solutions of Painlevé II on finite intervals of the real line, with Neumann boundary conditions, are constructed. Numerical experiments strongly suggest convergence of these sequences in a surprisingly wide range of cases, even ones where ordinary perturbation series fail to converge. These sequences are here labeled extraordinary because of their unusual properties. Each element of such a sequence is defined on its own interval. As the sequence (apparently) converges to a solution of the corresponding boundary value problem for Painlevé II, these intervals themselves (apparently) converge to the defining interval for that problem, and an associated sequence of constants (apparently) converges to the constant term in the Painlevé II equation itself. Each extraordinary sequence is constructed in a nonlinear fashion from a perturbation series approximation to the solution of a supplementary boundary value problem, involving a generalization of Painlevé II that arises in studies of electrodiffusion.
