A family of K-step Trigonometrically-fitted Block Falkner Methods is considered for the direct solution second order Oscillatory Initial value problems. As unique to methods, two main formulas (one method and one derivative) each k-step some additional formulas. This shall be adapted general oscillatory ordinary differential equations via multistep collocation technique. The idea employed in th...

Some new higher algebraic order symmetric various-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Basing on this formula, calculation of free parameters is performed to minimize the phase-lag. An explicit symmetric multistep method is presented. This method is of higher algebraic order and is fitted both exponentially and trigonomet...

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...

We present an improved version of the spline curve defined by H.-J. Wenz (1996) for the interpolation of 2D curve data. This trigonometrically blended spline is curvature continuous, interpolates 3D curve data, and is generated by convex combinations of circular arcs and straight line segments. As an application we show a method for rounding off the vertices of spatial polygonal lines and gener...

AC-operators were introduced by Berkson and Gillespie as a generalization in the context of well-boundedness of normal operators on Hilbert space. In this paper we explore some of the properties of these operators, such as the uniqueness of their splitting into real and imaginary parts, and their interpolation properties. We also examine the interpolation properties of the important subclass co...

Let E(·) : R → B(X) be the spectral decomposition of a trigonometrically well-bounded operator U acting on the arbitrary Banach space X, and suppose that the bounded function φ : T → C has the property that for each z ∈ T, the spectral integral R [0,2π] φ(e)dEz(t) exists, where Ez(·) denotes the spectral decomposition of the (necessarily) trigonometrically well-bounded operator (zU). We show th...

External fixation correction of angular deformities leads to secondary translation deformities when occurring around an axis located proximal or distal to the center of rotation of angulation (CORA); secondary length deformities result when correction occurs around an axis concave or convex to the CORA. With circular fixation, the hinge axis can be matched to the CORA. With monolateral fixation...