This article is cited in 2 papers

General numerical methods

Stability analysis of nonclassical difference schemes for nonlinear Volterra integral equations of the second kind

M. N. Botoroeva^ab, M. V. Bulatov<sup>a

a</sup> Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia
^b Irkutsk State University, 664003, Irkutsk, Russia

Abstract: A family of first- and second-order accurate noniterative numerical methods is constructed for solving systems of nonlinear Volterra integral equations of the second kind. The methods are examined for $A$-, $L$-, and $P$-stability. The conclusions are illustrated by numerical results obtained for test equations with stiff and oscillating components.

Key words: nonlinear Volterra integral equations of the second kind, difference schemes, $A$-stability, $L$-stability, $P$-stability.

UDC: 517.968.2

Received: 03.10.2022
Revised: 03.10.2022
Accepted: 20.01.2023

DOI: 10.31857/S0044466923060054

 English version: Computational Mathematics and Mathematical Physics, 2023, 63:6, 919–928

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