Implicit Runge- Kutta Methods for Second Kind Volterra Integral Equations.
Improvements of Euler-trapezoidal type inequalities with higher-order convexity and applications.
Indefinite integration of oscillatory functions
A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function , -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.
Inequalities of Ostrowski type and applications in numerical integration.
Integral inequalities and computer algebra systems.
Integration in higher-order finite element method in 3D
Integration of Iterated Integrals by Multistep Methods.
Integro-differential equations with time-varying delay
Integro-differential equations with time-varying delay can provide us with realistic models of many real world phenomena. Delayed Lotka-Volterra predator-prey systems arise in ecology. We investigate the numerical solution of a system of two integro-differential equations with time-varying delay and the given initial function. We will present an approach based on -step methods using quadrature formulas.
Interpolation and integration based on averaged values
We discuss recent results on constructing approximating schemes based on averaged values of the approximated function f over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of f over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.
Interpolation operators on the space of holomorphic functions on the unit circle
The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval , , have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general...
Interpolatorische Kubaturformeln [Book]
Is Gauss Quadrature Optimal for Analytic Functions?