Scholarlink

Abstract <p> We consider the Cauchy problem for a system of two first-order integro-differentialequations with memory in finite-dimensional Hilbert spaces, where the integral term contains adifference kernel. Such a mathematical model is typical for nonstationary electromagneticprocesses taking into account the electric field dispersion effects. To obtain an approximatesolution of the considered nonlocal problem, a transformation to a local Cauchy problem fora system of first-order equations is applied, based on approximating the difference kernel by a sumof exponentials. Two-level operator-difference schemes in Hilbert spaces are constructed andanalyzed for stability.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Operator-Difference Schemes for Systems of First-Order Integro-Differential Equations

  • 期刊论文

  • 发表日期：

    2025年7月1日

查看全文
  • P. N. Vabishchevich

摘要

Abstract

We consider the Cauchy problem for a system of two first-order integro-differentialequations with memory in finite-dimensional Hilbert spaces, where the integral term contains adifference kernel. Such a mathematical model is typical for nonstationary electromagneticprocesses taking into account the electric field dispersion effects. To obtain an approximatesolution of the considered nonlocal problem, a transformation to a local Cauchy problem fora system of first-order equations is applied, based on approximating the difference kernel by a sumof exponentials. Two-level operator-difference schemes in Hilbert spaces are constructed andanalyzed for stability.