非瞬时脉冲差分方程初值问题的单调迭代技巧
Monotone-iterative technique for an initial value problem for difference equations with non--instantaneous impulses
摘要：
本文研究一类特殊类型的差分方程。脉冲在某些点突然开始，它们的作用在给定的有限间隔内继续。这种类型的方程用于模拟真实过程。提出了一种近似求解非线性非瞬时脉冲差分方程初值问题的算法--单调迭代法。该算法的一个重要特点是：未知解的每一次逐次逼近都等于一个适当构造的具有非瞬时脉冲的线性差分方程的初值问题的唯一解，并给出了其显式表达式.证明了这两个序列都是收敛的，并且它们的极限是所考虑问题的最小解和最大解。
英文摘要：
In this paper a special type of difference equations is investigated. The impulses start abruptly at some points and their action continue on given finite intervals. This type of equations is used to model a real process. An algorithm, namely, the monotone iterative technique is suggested to solve the initial value problem for nonlinear difference equations with non-instantaneous impulses approximately. An important feature of our algorithm is that each successive approximation of the unknown solution is equal to the unique solution of an appropriately constructed initial value problem for a linear difference equation with with non-instantaneous impulses, and a formula for its explicit form is given. It is proved both sequences are convergent and their limits are minimal and maximal solutions of the considered problem.
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