Absolute stability domains of explicit methods of the Runge-Kutta family for the Dahlquist problem transformed to the best argument and its modifications

Title	Absolute stability domains of explicit methods of the Runge-Kutta family for the Dahlquist problem transformed to the best argument and its modifications
Authors	E. B. Kuznetsov¹, S. S. Leonov^{1, 2}, E. D. Tsapko¹ ¹Moscow Aviation Institute ²RUDN University
Annotation	The paper investigates the absolute stability domains of explicit methods of the Runge-Kutta family for the Dahlquist problem. The domain of absolute stability allows us to obtain an estimate of the step size of integration, which enables using explicit methods to get an approximate solution for a number of stiff initial problems without a significant increase in error. Also, the absolute stability domains for the Dahlquist problem transformed to the best argument and its modification constructed in the paper. The obtained results are in good agreement with existing theoretical researches.
Keywords	absolute stability domain, explicit Runge-Kutta methods, the Dahlquist problem, solution continuation method, the best argument, exponential best argument
Citation	Kuznetsov E. B., Leonov S. S., Tsapko E. D. ''Absolute stability domains of explicit methods of the Runge-Kutta family for the Dahlquist problem transformed to the best argument and its modifications'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 101-108. Available at: https://conf.svmo.ru/files/2023/papers/paper15.pdf. - Date of access: 03.12.2024.

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Absolute stability domains of explicit methods of the Runge-Kutta family for the Dahlquist problem transformed to the best argument and its modifications

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