COMPARING DIFFERENT METHODS OF DOUBLE INTEGRAL OF ITERATIONS AND DETERMINING THEIR ACCURACY TO APPLY FOR MONTE CARLO METHOD

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.