A note on Haselgrove’s method for numerical integration

A Note on Haselgrove's Method for Numerical Integration

An alternative set of weights is proposed for Niederreiter's generalization of Haselgrove's method for numerical integration. 1. In 1961, C. B. Haselgrove [1] introduced effective J-dimensional cubature formulas for a certain class of integrand functions over Gd i=[0,l]d) which were generalized by H. Niederreiter [2], [3]. But the generalized cubatures are not necessarily easy to handle. Here w...

A Numerical Integration Method by Using Generalized Series of Functions

a numerical integration method by using generalized series of functions

Monte Carlo Method for Numerical Integration Based on Sobol's Sequences

An efficient Monte Carlo method for multidimensional integration is proposed and studied. The method is based on Sobol’s sequences. Each random point in s-dimensional domain of integration is generated in the following way. A Sobol’s vector of dimension s (ΛΠτ point) is considered as a centrum of a sphere with a radius ρ. Then a random point uniformly distributed on the sphere is taken and a ra...

Convergence of product integration method applied for numerical solution of linear weakly singular Volterra systems

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.