论文标题
重新审视的渐近迭代方法
The Asymptotic Iteration Method Revisited
论文作者
论文摘要
渐近迭代方法（AIM）是一种用于分析和线性二阶方程的技术，尤其是在理论和数学物理学中经常出现的特征值问题。这项工作详细介绍了渐近迭代方法成功和失败的分析和数学理由。一个定理解释了为什么提出了为什么渐近迭代方法适用于特征值问题。作为副产品，还引入了一种新的程序，以生成无限的类别的确切可溶解微分方程的类别。
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical physics. The analysis and mathematical justifications of the success and failure of the asymptotic iteration method are detailed in this work. A theorem explaining why the asymptotic iteration method works for the eigenvalue problem is presented. As a byproduct, a new procedure to generate unlimited classes of exactly solvable differential equations is also introduced.
