Stability of solutions of systems of Volterra integral equations

2023/04/22 by I. V. Boykov, Boykov, Ilya, Vladimir Roudnev +3
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2304.11426

openalex publication_date 2023/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of Volterra linear integral equations are studied with perturbed right hand sides of the equations. These new sufficient conditions are expressed in terms of logarithmic norms of matrices consisting of coefficients of equations and derivatives of their kernels. For integro-differential Volterra equations we also provide sufficient conditions for stability of solutions when the initial conditions are perturbed.

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