Jñānābha‎, Vol. 50 (2) (2020), (273-282)

A STUDY ON THE EFFICIENCY OF PSEUDO RANDOM NUMBERS BY ANALYZING THE ERROR PROPAGATION WITH REFERENCE TO THE MONTE CARLO METHOD FOR NUMERICAL INTEGRATION

 

By

Saurabh Saxena 1, Ashish Arora 2 and Shweta Choudhary 3

Department of Applied Science and Humanities, ABES Engineering College

Campus -1, 19th KM Stone, NH-24, Ghaziabad-201009, Uttar Pradesh, India

Email: saxena22saurabh@gmail.com (Corresponding Author), ashish.arora@abes.ac.in, shweta.chaudhary@abes.ac.in

(Received : July 11, 2020 ; Revised: December 29, 2020)

 

 

Monte Carlo method is a powerful method for computing the value of complex integrals using probabilistic techniques and estimates the integrals or other quantities that can be expressed as an expectation by averaging the results of a high number of statistical trials.Its convergence rateO(√N), is independent of dimension and hence it is preferred for a wide range of high dimensional problems. In this article efficiency of random numbers is being analysed by comparing the error in the evaluation of bi-variate integral corresponding to different size of random numbers, and equi-spaced points by Monte Carlo method. Also analysed and discussed the propagation of error in every case.

 

2010 Mathematics Subject Classifications: 65C05, 65D30.

Keywords and phrases: Monte Carlo Method, Numerical Integration, Random Numbers, efficiency of random numbers.