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<p>This paper addresses the problem of nonparametric identification of nonlinear dynamical systems of the input-output type. This class of problems allows the original formulation to be reduced to solving linear one- and two-dimensional Volterra equations of the first kind (with variable limits of integration) with respect to asymmetric kernels. Issues concerning the well-posedness of the selected classes of integral equations are investigated. Central attention is given to questions related to the existence of exact solutions and to the development of methods for their construction.</p>

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On Some Linear Volterra Integral Equations of the First Kind and Their Numerical Solution

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Svetlana Solodusha,
  • Ekaterina Antipina

摘要

This paper addresses the problem of nonparametric identification of nonlinear dynamical systems of the input-output type. This class of problems allows the original formulation to be reduced to solving linear one- and two-dimensional Volterra equations of the first kind (with variable limits of integration) with respect to asymmetric kernels. Issues concerning the well-posedness of the selected classes of integral equations are investigated. Central attention is given to questions related to the existence of exact solutions and to the development of methods for their construction.