Multi-dimensional Monte Carlo Integrations Utilizing Mathematica

Chowdhury, Sujaul

/ ISBN 13: 9798337089232

Published by American Academic Press, 2025

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Synopsis:

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.

Bibliographic Details

Title: Multi-dimensional Monte Carlo Integrations ...
Publisher: American Academic Press
Publication Date: 2025
Binding: PAP
Condition: New