Multi-dimensional Monte Carlo Integrations Utilizing Mathematica

This book provides practical, hands-on demonstration of evaluation of multi-dimensional or high-dimensional definite integrals using Monte Carlo method. We have evaluated a large number of multi-dimensional definite integrals using Monte Carlo method. These are 2, 3, 5, 7 and 10 dimensional definite integrals. We have used mean value method for the evaluations. We have performed function evaluations at random values of the variables gathered as uniform random variates using inverse transform sampling method. We have performed symbolic computations using programs written in Mathematica. Very much smaller number of function evaluations is found to lead to much lower error compared to the case with uniform, non-random sampling i.e. without using Monte Carlo method. This is consistent with what we often hear about a virtue of Monte Carlo method in evaluating multi-dimensional or high-dimensional definite integrals.

Author:

Sujaul Chowdhury

Publisher:

American Academic Press

Publication Date:

Feb 15, 2025

Number of pages:

00122 pages

Binding:

Paperback or Softback

ISBN-10:

NA

ISBN-13:

9798337089232