Initial Value Problem of Ordinary Differential Equations: An Efficient Solution with Monte-Carlo Approach

An Efficient Solution for the Initial Value Problem of Ordinary Differential Equations using Monte-Carlo Approach

Abstract

The goal of this paper is to perform a computational investigation of a current Monte Carlo based algorithm to tackle initial value issue of ordinary differential equations (ODEs). Right off the bat the issues related with the current algorithm have been redressed by proposing another detailed algorithm. At that point the new algorithm has been connected to illuminate distinctive kinds of ODEs including straightforward, unequivocal coupled, certain and coupled system of first request ODEs. Besides the same has additionally been actualized to known physical systems, for example, Van der Pol equation and SIR pestilence show. The impediments of proposed algorithm have additionally been recognized by applying Lipschitz coherence check for a commendable ODE. At last it has been exhibited that it still exceptionally hard to propose a computationally effective algorithm to understand ODEs with significant precision utilizing Monte Carlo strategy.