This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous functions.

Abstract: Paper is devoted to the development of a method for approximating discontinuous functions by discontinuous splines and the construction of an algorithm for detecting discontinuity lines. The ...

1 Department of Mathematics, Binzhou University, Shandong, China. 2 Department of Mathematics, Neijiang Normal University, Sichuan, China. of functions [1] - [7] , computing the n-th iterate of ...

Commonly, in Ordinary Differential Equations courses, equations with impulses or discontinuous forcing functions are studied. In this context, the Laplace Transform of the Dirac delta function and ...

The extended Finite Element Method (XFEM) is derived from the traditional finite element method for discontinuous problems. It can simulate the behavior of cracks, which significantly improves the ...

This example illustrates some properties of splines. Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with ...

Conservation laws serve as a cornerstone in modelling the evolution of physical quantities such as mass, momentum and energy. Recent advances have placed a particular emphasis on systems where the ...