Jñānābha, Vol. 51 (2) (2021), (12-23)
Jñānābha, Vol. 51 (2) (2021), (12-23)
ALGORITHM TO SOLVE ODES USING LIE SYMMETRIES AND METHODS BASED ON FIRST INTEGRALS
By
Vishwas Khare¹ and M. G. Timol²
¹Department of Mathematics, SSR College of ACS Silvassa-396230, U.T. of DNH and DD, India.
²Ex Professor, Department of Mathematics, Veer Narmad South Gujarat University, Surat-395007, Gujarat, India.
Email:vskssr@gmail.com, mgtimol@gmail.com
(Received : August 19, 2020; In format : March 19, 2021; Revised in final form: September 20, 2021)
DOI: https://doi.org/10.58250/Jnanabha.2021.51202
Abstract
The algorithm is developed in Computer algebra system, open source SageMath software which helps in finding the first integrals of ODEs of order 2 that admit Lie algebra so(3) and the first integrals of third-order ODEs that admit four or more than four symmetry generators. The application of algorithm is illustrated through examples. The advantage of the present algorithm is that, it is universal as SageMath is a free open-source mathematics software system licensed under the GPL. By giving input of values of infinitesimal generators in the interactive window the user get values of Qis and Wijks as output.
2020 Mathematical Sciences Classification: 34-04, 76M60.
Keywords and Phrases: Lie symmetry, Second and third order ODE, SageMath software, characteristic.