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Absolute stability of the explicit scheme of the Euler method for problems transformed to the best argument and its modification

TitleAbsolute stability of the explicit scheme of the Euler method for problems transformed to the best argument and its modification
AuthorsE. D. Tsapko1, S. S. Leonov1, 2, E. B. Kuznetsov1
1Moscow Aviation Institute
2Peoples’ Friendship University of Russia
AnnotationWhen modeling physical and technological processes, researchers often face the need to solve stiff initial tasks. As a rule, explicit numerical methods of solving such problems are unsuitable due to insufficient stability. The most frequently used best argument turns out to be hardly applicable for solving problems whose growth rate of integral curves is close to exponential. The authors previously proposed a modification of the best argument, which made it possible to smooth out this disadvantage. In this paper, estimates of the absolute stability of the explicit scheme of the Euler method in solving problems transformed to a modified best argument are given. The approbation of the obtained theoretical estimates is carried out on the example of solving a test problem.
Keywordsabsolute stability, stability domain, Dahlquist test problem, difference scheme, explicit Euler method, initial problem, solution continuation method, best argument, modified best argument.
CitationTsapko E. D., Leonov S. S., Kuznetsov E. B. ''Absolute stability of the explicit scheme of the Euler method for problems transformed to the best argument and its modification'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 14-18, 2022). Saransk: SVMO Publ, 2022. - pp. 210-213. Available at: https://conf.svmo.ru/files/2022/papers/paper32.pdf. - Date of access: 30.11.2022.