On Simpson's inequality and applications.
On smoothing conditions of multivariate splines.
On some composite schemes of time integration in structural dynamics
Numerical simulations of time-dependent behaviour of advances structures need the analysis of systems of partial differential equations of hyperbolic type, whose semi-discretization, using the Fourier multiplicative decomposition together with the finite element or similar techniques, leads to large sparse systems of ordinary differential equations. Effective and robust methods for numerical evaluation of their solutions in particular time steps are required; thus still new computational schemes...
On some quadrature rules with Laplace end corrections
We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σi=1∞ f(i + 1/2) where f ∈ C 6 with its sixth derivative of constant sign on [m, ∞) and ∫ m∞ f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections,...
On the approximation of an integral by a sum of random variables.
On the arc length of parametric cubic curves.
On the asymptotics of mean value points for some finite-difference operators.
On the axonometrical projection in the computer graphics.
On the best approximation properties of -smooth functions on an interval of the real axis (to the phenomenon of unsaturated numerical methods).
On the calculation of approximate fekete points: the univariate case.
On the calculation of elliptic integrals of the second and third kinds
On the computation of Aden functions
The paper deals with the computation of Aden functions. It gives estimates of errors for the computation of Aden functions by downward reccurence.
On the computation of Riccati-Bessel functions
The paper deals with the computation of Riccati-Bessel functions. A modification of Miller method is presented together with estimates of relative errors.
On the computation of the GCD of 2-D polynomials
The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
On the computation of zeros and turning points of Bessel functions
On the Condition Number of some Gram Matrices Arising from Least Squares Approximation in the Complex Plane.
On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey’s Method of Transport (MoT) (respectively the second author’s ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the gas kinetic derivation...
On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey's Method of Transport (MoT) (respectively the second author's ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the...
On the Construction of Multi-Dimensional Embedded Cubature Formulae.
On the Construction of Sufficient Refinements for Computation of Topological Degree.