This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the number of nodes can be a priori selected. The analysis is also used to design an automatic integrator that can be employed without any knowledge of the function involved in the problem. Several numerical examples, which confirm the reliability of this strategy, are reported
AbstractInterpolatory integration rules of numerical stability are presented for approximating Cauch...
The numerical solution of highly oscillatory initial value problems of second order with a unique hi...
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule a...
It is well known that the trapezoidal rule converges geometrically when applied to analytic function...
Consider the evaluation of If:=^^f201f(x) dx . Among all the quadrature rules for the appr...
The error in the trapezoidal rule quadrature formula can be attributed to discretization in the inte...
Following on from our recent investigation of series and products using the Euler–Maclaurin formula,...
AbstractIn the present paper, we use a generalization of the Euler–Maclaurin summation formula for i...
In many applied problems, efficient calculation of quadratures with high accuracy is required. The e...
A sigmoidal transformation is a one-to-one mapping of the compact interval [0,1] onto itself whose ...
In this paper we propose a method for computing the Faddeeva function $w(z) := \re^{-z^2}\erfc(-\ri...
In this paper we are interested in the approximation of fractional powers of self-adjoint positive o...
AbstractThis paper is concerned with the numerical integration of functions by piecewise polynomial ...
We want to numerically approximate coefficients in a Fourier series. The first step is to see how th...
When it is not possible to integrate a function we resort to Numerical Integration. For example the ...
AbstractInterpolatory integration rules of numerical stability are presented for approximating Cauch...
The numerical solution of highly oscillatory initial value problems of second order with a unique hi...
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule a...
It is well known that the trapezoidal rule converges geometrically when applied to analytic function...
Consider the evaluation of If:=^^f201f(x) dx . Among all the quadrature rules for the appr...
The error in the trapezoidal rule quadrature formula can be attributed to discretization in the inte...
Following on from our recent investigation of series and products using the Euler–Maclaurin formula,...
AbstractIn the present paper, we use a generalization of the Euler–Maclaurin summation formula for i...
In many applied problems, efficient calculation of quadratures with high accuracy is required. The e...
A sigmoidal transformation is a one-to-one mapping of the compact interval [0,1] onto itself whose ...
In this paper we propose a method for computing the Faddeeva function $w(z) := \re^{-z^2}\erfc(-\ri...
In this paper we are interested in the approximation of fractional powers of self-adjoint positive o...
AbstractThis paper is concerned with the numerical integration of functions by piecewise polynomial ...
We want to numerically approximate coefficients in a Fourier series. The first step is to see how th...
When it is not possible to integrate a function we resort to Numerical Integration. For example the ...
AbstractInterpolatory integration rules of numerical stability are presented for approximating Cauch...
The numerical solution of highly oscillatory initial value problems of second order with a unique hi...
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule a...
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