This paper deals with the use of trigonometric splines (also call Schoenberg’s polynomials) in order to increasing the performances of a nonlinear closed-loop system. In the first part, it is recalled that for linear systems, the couple ”setting time/overshoot” can be largely improved if a path planning is used instead of a classical step input. The concept of trigonometric splines is then intr...

This paper proposes a numerical method to obtain an approximation solution for the time-fractional Schrödinger Equation (TFSE) based on combination of cubic trigonometric B-spline collocation and Crank-Nicolson scheme. The fractional derivative operator is described in Caputo sense. L1−approximation used discretization. Using Von Neumann stability analysis, proposed technique shown be condition...

Let φ be a compactly supported refinable function in L2(R) such that the shifts of φ are stable and φ̂(2ξ) = â(ξ)φ̂(ξ) for a 2π-periodic trigonometric polynomial â. A wavelet function ψ can be derived from φ by ψ̂(2ξ) := e−iξ â(ξ + π)φ̂(ξ). If φ is an orthogonal refinable function, then it is well known that ψ generates an orthonormal wavelet basis in L2(R). Recently, it has been shown in the liter...

This paper presented the G1 cubic trigonometric spline function with three shape parameters that generate a constrained curve interpolates 2D data. The purpose of this research is to ensure generated passes through all data point yet satisfied cases line constraints given. are: must lie above Li below and lastly, between two lines Li,1 Li,2. A simpler theorem implemented involving roles paramet...