Determining equations for infinitesimal transformation of second and third-order ODE using algorithm in open-source SageMath
Authors :
Vishwas Khare 1 * and M.G. Timol 2
Author Address :
1 S.S.R. College of Arts Commerce and Science Silvassa, Silvassa-396230, India.
*Corresponding author.
Abstract :
To find exact solutions of nonlinear Ode using Lie symmetry technique it is required to find infinitesimal generator of the group admitted by differential equation, which becomes cumbersome if done manually.
The purpose of this paper is to develop algorithm in open-source SageMath to find the determining equations for infinitesimal transformation of Second and Third-order ODE which on solving gives value of infinitesimal.
The algorithm developed in the paper is prepared in python language. The codes given in algorithm can be used by typing or by downloading the .odt file by using link
\url{https://drive.google.com/open?id=19T5FHV89Z41um7_LbvsNIgnyF0_hlfJT}.The codes given in .odt file can then copied and pasted in Sage Cell, SageMath cloud ( CoCalc - Collaborative Calculation and Data Science) or in SageMath - Open-Source Mathematical Software System and run it. \\\
By giving input of differential equation in interactive window the user can get the output as determining equations for infinitesimal transformation.
Keywords :
Infinitesimal transformation, Lie symmetry, Ode of second and third order, SageMath software.
DOI :
Article Info :
Received : January 24, 2020; Accepted : April 17, 2020.
