论文标题
反转公式及其对第一类多维伏特拉方程的有限维度类似物
Inversion formulas and their finite-dimensional analogs for multidimensional Volterra equations of the first kind
论文作者
论文摘要
本文着重于解决第一类的一类Volterra方程，其特征在于所有集成限制的可变性。引入了与识别用于构建“输入输出”类型非线性动力学系统积分模型的非对称内核有关的问题，以Volterra多项式形式的形式构建了积分模型。考虑系统的输入扰动是时间的向量函数时。为了解决识别问题，以前引入的持续时间H（网格步骤）的测试信号以偏差参数的线性组合形式使用。本文展示了一种获得所需解决方案的方法，为一维情况开发了一种步骤方法。建立了提供解决方案所需平滑度的匹配条件。考虑了基于中间矩形公式的研究积分方程的网格类似物。
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric kernels for constructing integral models of nonlinear dynamical systems of the "input-output" type in the form of Volterra polynomials. The case when the input perturbation of the system is a vector function of time is considered. To solve the identification problem, previously introduced test signals of duration h (mesh step) are used in the form of linear combinations of Heaviside functions with deviating arguments. The paper demonstrates a method for obtaining the desired solution, developing a method of steps for a one-dimensional case. The matching conditions providing the desired smoothness of the solution are established. The mesh analogs of the studied integral equations based on the formulas of middle rectangles are considered.
