Numerical Integration of locally Peaked Bivariate Functions

Abstract

The aim of this paper is to compare the relative accuracies between deterministic and stochastic methods for solving bounded integrals numerically to observe which methods tend to function well and converge to a small amount of error based on computational resources. For the deterministic method, the Gauss-Legendre quadrature method has been selected and for the stochastic method, the Monte Carlo integration has been selected. For each case, the number of variables will be adjusted to observe the effect on error. For the Gauss-Legendre quadrature method the permutations increased with the inaccuracy of 9% when the number of nodes increased to 3 but was reduced by 90% and later on the error depicted a drop as the number of nodes raised further. For the stochastic method, that was chosen from large sample size, the inaccuracy was found to be inversely proportional to the sample size. This concluded that the monte-carlo approach was not affected by the impact of dimensionality moreover, deterministic method also seemed to overcome the dimensionality constraint.