On the algorithmic linearizability of nonlinear ordinary differential equations

Solving nonlinear ordinary differential equations is one of the fundamental and practically important research challenges in mathematics. However, the problem of their algorithmic linearizability so far remained unsolved. In this contribution, we propose a solution of this problem for a wide class of nonlinear ordinary differential equation of arbitrary order. We develop two algorithms to check if a nonlinear differential equation can be reduced to a linear one by a point transformation of the dependent and independent variables. In this regard, we have restricted ourselves to quasi-linear equations with a rational dependence on the occurring variables and to point transformations. While the first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra, the second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of our algorithms is discussed and evaluated using several examples. © 2019 Elsevier Ltd

Авторы
Lyakhov D.A.1 , Gerdt V.P. 2, 3 , Michels D.L.1, 4
Издательство
Academic Press
Язык
Английский
Страницы
3-22
Статус
Опубликовано
Том
98
Год
2020
Организации
  • 1 Computational Sciences Group, KAUST, Thuwal, Saudi Arabia
  • 2 Group of Algebraic and Quantum Computations, Joint Institute for Nuclear Research, Dubna, Russian Federation
  • 3 Peoples' Friendship University of Russia (RUDN University), Moscow, Russian Federation
  • 4 Computer Science Department, Stanford University, Stanford, CA, United States
Ключевые слова
Algorithmic linearization test; Differential Thomas decomposition; Lie symmetry algebra; Ordinary differential equations; Point transformation; Tremblay-Turbiner-Winternitz system
Дата создания
10.02.2020
Дата изменения
10.02.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/56494/