Published in Numerical Algorithms
The sinc-Gaussian sampling formula is used to approximate an analytic function, which satisfies a growth condition, using only finite samples of the function. The error of the sinc-Gaussian sampling formula decreases exponentially with respect to N, i.e., N− 1/2e−αN, where α is a positive number. In this paper, we extend this formula to allow the a...
Published in Numerical Algorithms
Let Ω be an open region in ℝd, d ≥ 2, that is diffeomorphic to 𝔹d. Consider solving −Δu + γu = 0 on Ω with the Neumann boundary condition ∂u∂n=b⋅,u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin...
Published in Numerical Algorithms
Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone operator. The strong convergence of the iterative sequence generated by our method is established in real Hilbert spaces. Our method uses computationally inexpensive Armijo-type linesearch procedure to compu...
Published in Numerical Algorithms
Let x0,x1, ⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xm ≠ xj, for m ≠ j) and let ym,k, for m = 0, 1, ⋯ , n, and k = 0, 1, ⋯ , rm, with rm ∈ IN, be given real numbers. It is known that there exists a unique polynomial pN− 1 of degree N − 1 with N=∑m=0n(rm+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepack...
Published in Numerical Algorithms
The goal of this paper is to present a new scheme based on the stochastic arithmetic (SA) to find the optimal convergence control parameter, the optimal iteration and the optimal approximation of the homotopy analysis method (HAM). This scheme is called the CESTAC1 method. Also, the CADNA2 library is applied to implement the CESTAC method on the pr...
Published in Numerical Algorithms
Implicitly defined fully nonlinear differential equations can admit solutions which have only finitely many derivatives, making their solution via analytical or numerical techniques challenging. We apply the optimal homotopy analysis method (OHAM) to the solution of implicitly defined ordinary differential equations, obtaining solutions with low er...
Published in Numerical Algorithms
In the present paper, we study a new kind of Bernstein-Kantorovich-type operators. Here, we discuss a uniform convergence estimate for this modified form. Also, some direct estimates, which involve the asymptotic-type results, are established. Some numerical examples which show the relevance of the results are considered.
Published in Numerical Algorithms
The exponential stability and the polynomial stability have been well studied for the exact and numerical solutions of the stochastic pantograph differential equations (SPDEs), while the result on the general decay stabilities is insufficient for SPDEs. In this paper, the sufficient conditions of the almost sure stability with general decay rate of...
Published in Numerical Algorithms
This paper deals with generalized centro-invertible matrices introduced by the authors in Lebtahi et al. (Appl. Math. Lett. 38, 106–109, 2014). As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generaliz...
Published in Numerical Algorithms
