Related papers: A novel hybrid method for equilibrium problems and…
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…
Optimal balance is a non-asymptotic numerical method to compute a point on the slow manifold for certain two-scale dynamical systems. It works by solving a modified version of the system as a boundary value problem in time, where the…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
In this paper, we propose a hybrid method that combines finite element method (FEM) and physics-informed neural network (PINN) for solving linear elliptic problems. This method contains three steps: (1) train a PINN and obtain an…
In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…
In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert…
This study delves into equilibrium problems, focusing on the identification of finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field,…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life, to address this issue, we studied…
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
In this paper, an easy-to-implement and computationally effective numerical method based on the new orthogonal hybrid functions is developed to solve system of fractional order differential equations numerically. The new orthogonal hybrid…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…
In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family…