Explicit Methods for Integrating Stiff Cauchy Problems

Abstract: An explicit method for solving stiff Cauchy problems is proposed. The method relies on explicit schemes and a step size selection algorithm based on the curvature of an integral curve. Closed-form formulas are derived for finding the curvature. For Runge–Kutta schemes with up to four stages, the corresponding sets of coefficients are given. The method is validated on a test problem with a given exact solution. It is shown that the method is as accurate and robust as implicit methods, but is substantially superior to them in efficiency. A numerical example involving chemical kinetics computations with 9 components and 50 reactions is given. © 2019, Pleiades Publishing, Ltd.

Авторы
Belov A.A. 1, 2 , Kalitkin N.N.3 , Bulatov P.E.1 , Zholkovskii E.K.1
Журнал
Номер выпуска
2
Язык
Английский
Страницы
230-234
Статус
Опубликовано
Том
99
Год
2019
Организации
  • 1 Faculty of Physics, Lomonosov Moscow State University, Moscow, 119992, Russian Federation
  • 2 RUDN University, Moscow, 117198, Russian Federation
  • 3 Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russian Federation
Дата создания
19.07.2019
Дата изменения
19.07.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/38726/