On methods for determining the domains of absolute stability of the explicit Euler method for some classes of nonautonomous differential equations

Title	On methods for determining the domains of absolute stability of the explicit Euler method for some classes of nonautonomous differential equations
Authors	E. B. Kuznetsov¹, S. S. Leonov¹ ¹Moscow Aviation Institute
Annotation	In this paper authors consider the absolute stability of the explicit Euler method for solving of an initial value problem for the nonautonomous Dahlquist equation. The equation of this problem, in comparison with the traditional one, is supplemented with a linear summand with respect to the argument. Authors give an original method of constructing absolute stability domains of the explicit Euler method for certain classes of initial value problems and defined estimates of the integration step size for the founded regions. All the results obtained are in good agreement with those already available in the scientific literature.
Keywords	absolute stability domain, Eulers explicit method, Cauchy problem, Dahlquist equation, ordinary differential equations.
Citation	Kuznetsov E. B., Leonov S. S. ''On methods for determining the domains of absolute stability of the explicit Euler method for some classes of nonautonomous differential equations'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 129-134. Available at: https://conf.svmo.ru/files/2025/papers/paper26.pdf. - Date of access: 30.08.2025.

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On methods for determining the domains of absolute stability of the explicit Euler method for some classes of nonautonomous differential equations

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