We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. Firstand second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition.

In this paper, we present an iterative method for fixed point problems and variational inequality problems. Our method is based on the so-called extragradient method and viscosity approximation method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for monotone mapping.

In this paper, we introduce a probabilistic numerical scheme for a class of parabolic and elliptic fully non-linear PDEs in bounded domains. In the main result, we provide the convergence of a discrete-time approximation to the viscosity solution of a fully non-linear parabolic equation by assuming that comparison principle holds for the PDE.

This paper considers the computational issue of the optimal stopping problem for the stochastic functional differential equation treated in [4]. The finite difference method developed by Barles and Souganidis [2] is used to obtain a numerical approximation for the viscosity solution of the infinite dimensional Hamilton-Jacobi-Bellman variational inequality (HJBVI) associated with the optimal st...

The purpose of this paper is, by using viscosity approximation methods, to find a common element of the set of solutions of an equilibrium problem and the set of fixed point of a nonexpansive mappings in a Hilbert space and to prove, under suitable conditions, some strong convergence theorems for approximating a solution of the problem under consideration. AMS (MOS) Subject Classification. 47H0...

In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem. The results obtained in this paper generalize and improve the recent ones announced by many others. c ©2017 All rights ...

Our study is dedicated to the probabilistic representation and numerical approximation of solutions of coupled systems of variational inequalities. We interpret the unique viscosity solution of a coupled system of variational inequalities as the solution of a one-dimensional constrained BSDE with jumps. This new representation allows for the introduction of a natural probabilistic numerical sch...

The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to λ-strict pseudocontractions in p-uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.

The aim of this paper is to prove a new iterative sequence {xn} under some sufficient and necessary conditions converges strongly to a common fixed point of asymptotically nonexpansive mappings {Ti}i=1 by using viscosity approximation methods. Our results extend and improve some recent results. Mathematics Subject Classification: 47H09, 47H10

In this paper, we establish a composite iteration scheme by the viscosity approximation method for finding a common element of the set of zero points of an accretive operator and the set of solutions of an equilibrium problem in the framework of a Hilbert space. Mathematics Subject Classification: 39B12, 47H06, 47H10