On one method of numerical integration

A Numerical Integration Method by Using Generalized Series of Functions

a numerical integration method by using generalized series of functions

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.

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...

Numerical Integration Method Based on Particle Swarm Optimization

In this paper, a novel numerical double integration method based on Particle Swarm Optimization (PSO) was presented. PSO is a technique based on the cooperation between particles. The exchange of information between these particles allows to resolve difficult problems. This approach is carefully handled and tested with an illustrated example.