Методи розв’язування початкової задачі з двосторонньою оцінкою локальної похибки: Fìz.-mat. model. ìnf. tehnol. 2021, 33:88-92

• Date: 2021
• Main Authors: Pelekh, Yaroslav, Kunynets, Andrii, Beregova, Halyna, Magerovska, Tatiana
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: задача Коші; однокрокові методи; ланцюгові дроби; вкладені методи; двостороння апроксимація; локальна похибка
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/208
• Journal Title: Physico-mathematical modeling and informational technologies

Numerical methods for solving the initial value problem for ordinary differential equations are proposed. Embedded methods of order of accuracy 2(1), 3(2) and 4(3) are constructed. To estimate the local error, two-sided calculation formulas were used, which give estimates of the main terms of the error without additional calculations of the right-hand side of the differential equation, which favorably distinguishes them from traditional two-sided methods of the Runge- Kutta type. References Skorobogatko, V. Ya. (1983). The theory of branching chain fractions and its application in computational mathematics. M.: Nauka. (in Russian). Gorbunov, A. D., Shakhov, Yu. A. (1963). On the approximate solution of the Cauchy problem for ordinary differential equations with a predetermined number of correct signs. I. J. calculated. mat. and mathematics. phys., 3(2), 239-253. (in Russian). DOI https://doi.org/10.1016/0041-5553(63)90023-5 Dobronets, B. S., Shaidurov, V. V. (1990). Bilateral numerical methods. Novosibirsk: Science. (in Russian). Krylov, V. I., Bobkov, V. V., Monastyrny, P. I. (1977). Computational methods. Volume II. M.: Nauka. (in Russian).