In this paper, we introduce a modified projection method and give a strong convergence theorem for solving variational inequality problems in real Hilbert spaces. Under mild assumptions, there exists a novel line-search rule that makes the …

In this paper, we conduct an in-depth investigation of the structural intricacies inherent to the Invariant Energy Quadratization (IEQ) method as applied to gradient flows, and we dissect the mechanisms that enable this method to keep linearity …

In this paper, we first propose a version of FISTA, called C-FISTA type gradient projection algorithm, for quasi-variational inequalities in Hilbert spaces and obtain linear convergence rate. Our results extend the results of Nesterov for C-FISTA …

We study the reconstruction of an unknown/inaccessible smooth inner boundary from the knowledge of the Dirichlet condition (temperature) on the entire boundary of a doubly connected domain occupied by a two-dimensional homogeneous anisotropic …

An operator-splitting finite element scheme for the time-dependent radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite element method are used for …

Most of the time, while deblurring an image, we need the restored image’s intensities to be precisely non-negative. However, it has been noted that using current numerical techniques to solve the problem could produce outcomes that are not always …

In this paper, a class of Runge-Kutta methods for solving neutral delay differential equations (NDDEs) is proposed, which was first introduced by Bassenne et al. (J. Comput. Phys. 424, 109847, 2021) for ODEs. In the study, the explicit Runge-Kutta …

The randomized Kaczmarz method, along with its recently developed variants, has become a popular tool for dealing with large-scale linear systems. However, these methods usually fail to converge when the linear systems are affected by heavy …

In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math. 367, 112485 …

In this article, we deal with nonconvex fractional programming problems involving E-differentiable functions $$(FP_E)$$ ( F P E ) . The so-called E-Karush-Kuhn-Tucker sufficient E-optimality conditions are established for nonsmooth optimization …

In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision …

In this paper, we intend to formulate and solve Cauchy problems for the Brinkman equations governing the flow of fluids in porous media, which have never been investigated before in such an inverse formulation. The physical scenario corresponds to …

Nonlinear coupled reaction-diffusion systems often arise in cooperative processes of chemical kinetics and biochemical reactions. Owing to these potential applications, this article presents an efficient and simple meshless approximation scheme to …

Integrodifference equations are discrete-time counterparts to reaction-diffusion equations and have various applications in, e.g., theoretical ecology. Their behavior is often illustrated using numerical simulations, which require a spatial …

In this paper, based on a nonmonotone derivative-free line search, we propose a two-step Broyden-like method (denoted by TS-BLM) for solving the nonlinear equations. TS-BLM computes one quasi-Newton step at the beginning iterations. When the …

We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate …

This paper presents a Legendre-Galerkin spectral method to compute the solution of a distributed optimal control problem (OCP) constrained by the biharmonic equation on regular and irregular domains. First, the optimality system is obtained by the …

For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge–Kutta methods and continuous-stage Runge–Kutta methods …

Robust fused lasso (RFlasso) estimation plays an important role in regression analysis because it can deal with variable selection problems more robust than fused lasso for the case containing non-Gaussian distribution outliers, especially when …