A novel numerical solution to lane-emden type equations using monte carlo technique

Abstract

Monte Carlo (MC) methods are increasingly recognized as severe in many computational scientific fields and have diverse applications in many branches of science. This paper systematically provides two computational algorithms based on MC methods to solve different forms of Lane-Emden (LE) type equations. The proposed algorithms introduce solutions to 11 LE equations under various complex conditions. The performance and comparative study of numerical solutions based on the MC algorithms were computationally analyzed using other numerical/analytical methods available in the literature. We find that the MC solutions agree with the exact or Runge–Kutta solutions and different numerical methods applied to solve these equations.