Abstract:
The accuracy and efficiency of computing multiple integrals is a very important problem
that arises in many scientific,financial and engineering applications.The research conducted in this thesis is designed to compare Trapezoidal,rectangular(direct iteration) and
Simpson rule’s with Monte Carlo simulation of double integral.The fundamental aim is
to assess techniques for numerically evaluating double integrals with high accuracy. From
the comparison, we obtained that Simpson’s rule for variable limit is better approximation
than Monte Carlo method.An application is the Monte Carlo method, which samples the
integrand at n randomly selected points and attempts to compute the mean value of the
integrand on the entire domain,and usually converge faster for quintuple multiple integrals
and higher, and yield greater accuracy for the same number of function evaluations than
repeated integrals using one dimensional method.
