Ahmed Tijini

Sextic spline solution of fifth-order boundary value problems

There are few techniques to numerically solve fifth-order boundary-value problems (BVPs). In this paper two sextic spline collocation methods are developed and analyzed. The first one uses spline interpolants and the second is based on spline quasi-interpolants. They are both proved to be second-order convergent. Numerical results verify the order of convergence predicted by the analysis.

Spline collocation method for solving linear sixth-order boundary-value problems

There are few techniques to numerically solve sixth-order boundary-value problems. In this paper, septic-spline collocation method based on spline interpolants is developed and analysed. There is proved to be second-order convergent. Numerical results verify the order of convergence predicted by the analysis. We also give a comparison of this with those developed by El-Gamel, Cannon and Zayed in 2003 and Akram and Siddiqi in 2006.

A SIMPLE METHOD FOR SMOOTHING FUNCTIONS AND COMPRESSING HERMITE DATA

Abstract Let τ=(a=x0<x1<⋅⋅⋅<xn=b) be a partition of an interval [a,b] of R, and let f be a piecewise function of class Ck on [a,b] except at knots xi where it is only of class

A normalized basis for C1 cubic super spline space on Powell-Sabin triangulation

C^{k_{i}}

A general family of third order method for finding multiple roots

, ki≤k. We study in this paper a novel method which smooth the function f at xi, 0≤i≤n. We first define a new basis of the space of polynomials of degree ≤2k+1, and we describe algorithms for smoothing the function f. Then, as an application, we give a recursive computation of classical Hermite spline interpolants, and we present a method which allows us to compress Hermite data. The most part of these results are illustrated by some numerical examples.

Superconvergent trivariate quadratic spline quasi-interpolants on Worsey-Piper split

In this paper, we describe the construction of a suitable normalized B-spline representation for bivariate C^1 cubic super splines defined on triangulations with a Powell-Sabin refinement. The basis functions have local supports, they form a convex partition of unity, and every spline is locally controllable by means of control triangles. As application, discrete and differential quasi-interpolants of optimal approximation order are developed and numerical tests for illustrating theoretical results are presented.

Construction of quintic Powell–Sabin spline quasi-interpolants based on blossoming

Abstract In this paper, we describe a general family of iterative methods for approximating a multiple root z with multiplicity m of a complex defined function. Almost of the family of the methods existing in the literature that use two-function and one-derivative evaluations are a special choice of this general method. We give some conditions to have the third order of convergence and we discuss how to choose a small asymptotic error constant which may be affect the speed of the convergence. Using Mathematica with its high precision compatibility, we present some numerical examples to confirm the theoretical results.

Sextic spline collocation methods for nonlinear fifth-order boundary value problems

In this paper we use Normalized trivariate Worsey-Piper B-splines recently constructed by Sbibih et?al. (2012) and the method proposed in Sbibih et?al. (2013) to give a new representation of Worsey-Piper Hermite interpolant of any piecewise polynomial of class at least C 1 over the Worsey-Piper split in terms of its polar forms. Using this representation we construct several superconvergent discrete quasi-interpolants. The construction that we present in this work is a generalization of the one presented in Sbibih et?al. (2012) with other properties.

A simple method for constructing integro spline quasi-interpolants

Abstract By blossoming Marsden’s identity, we investigate local quasi-interpolation schemes for C 2 -continuous quintic Powell–Sabin splines represented with a normalized B-spline basis. As applications, various families of discrete and differential quasi-interpolants reproducing quintic polynomials are presented.

Trivariate spline quasi-interpolants based on simplex splines and polar forms

In this paper, two sextic-spline collocation methods are developed and analysed for approximating solutions of nonlinear fifth-order boundary-value problems. The first method uses a spline interpolant and the second one is based on a spline quasi-interpolant, which are constructed from sextic splines. They are both proved to be second-order convergent. Numerical results confirm the order of convergence predicted by the analysis. It has been observed that the methods developed in this paper are better than the others given in the literature.