ABSTRACT We introduce a finite difference and q-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear second-order difference or q-difference equation subject to a ‘terminating condition’, which is precisely defined. When a difference or q-difference equation has a polynomial solution, we show how to find the second solution.

中文翻译：

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一种离散的q渐近迭代方法

摘要 我们介绍了 Ciftci、Hall 和 Saad 的渐近迭代方法的有限差分和 q 差分类似物。我们给出了满足严格定义的“终止条件”的一般线性二阶差分或 q 差分方程的多项式解存在的充分必要条件。当差分或 q 差分方程有多项式解时，我们将展示如何找到第二个解。