A Method for 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 Method for the Numerical Integration of Ordinary Differential Equations

where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...

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...