The aim of this article is to introduce the Douglas–Rachford splitting method with linearization to solve the split feasibility problem (SFP). Our proposed method includes two existing methods in work of Tang et al. and Wang as special cases. T...
The asphalt mixture splitting test is one of the most important methods for measuring asphalt’s tensile properties. To characterize the limitations of the traditional splitting test and the influence of the specimen size and loading conditions...
This article is concerned with the convergence properties of the Strang splitting method for the Degasperis-Procesi equation, which models shallow water dynamics. The challenges of analyzing splitting methods for this equation lie in the fact that th...
For solving the continuous Sylvester equation, a class of Hermitian and skew-Hermitian based multiplicative splitting iteration methods is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous...
In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear...
Recovering the past movement of a contaminant plume from measurements of its current values is a challenging problem in hydrology. Moreover, modeling the movement of a contaminant plume backwards is an ill-posed problem due to the unstable and non-un...
Aiming to solve the problem of dense-frequency signals in the power system caused by the growing proportion of new energy, this paper proposes a dense-frequency signal-detection method based on the primal–dual splitting method. After establishi...
The regularization method has a direct impact on the accuracy of the reconstructed sound field in the process of inverse calculation of near−field acoustic holography using the equivalent source method. To expand the frequency range of sound fi...
This paper introduces an alternative method for determining the shear strength parameters of concrete materials, specifically the rectangular section splitting method, to ascertain the shear strength parameters of concrete materials. Based on the Moh...
The symmetric successive overrelaxation (SSOR) and symmetric accelerated overrelaxation (SAOR) are conventional iterative methods for solving linear equations. In this paper, novel approaches are presented by combining a splitting–linearizing m...
By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Sinc...
A two-step simplified modulus-based matrix splitting iteration method is presented for solving the linear complementarity problem. According to general matrix splitting and special matrix splitting, a general convergence analysis and a specific conve...
In order to reduce the cost of wellheads, the production rate of the gas wells in the Hechuan Gas Field are mostly measured in groups, which raises a stringent barrier for industries to determine the production rate of each single well. The technique...
In this paper, a tensor splitting AOR iterative method for solving the
By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions o...
Most of the tunnel excavation methods involve the use of explosion and vibration techniques that is not feasible in urban areas due to unavoidable production of noise, vibration, and dust. The environmental considerations of tunneling projects in urb...
This paper proposes a partition of unity method (PUM) based on KDFCM (KDFcmPUM) that can be implemented to solve the dense matrix problem that occurs when the radial basis function (RBF) interpolation method deals with a large amount of scattered dat...
In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s...
A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (...
The purpose of this work is to study the efficient numerical solvers for time-dependent conservative space fractional diffusion equations. Specifically, for the discretized Toeplitz-like linear system, we aim to study efficient preconditioning based...
Aroma is one of the most important quality indicators of tea. However, this evaluation method is a subjective one. In this study, the volatiles of tea with 5 types were determined by headspace solid-phase micro-extraction (HS-SPME) combined with gas...
The reflected–forward–backward splitting (RFBS) method is well-established for solving monotone inclusion problems involving Lipschitz continuous operators in Hilbert spaces, where it converges weakly under mild assumptions. Extending thi...
The benefits and properties of iterative splitting methods, which are based on serial versions, have been studied in recent years, this work, we extend the iterative splitting methods to novel classes of parallel versions to solve nonlinear fractiona...
This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection–diffusion–reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive id...
In this paper, we discuss the different splitting approaches to numerically solve the Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einstein condensate (BEC). This system is formed of coupled mean-field equati...
CuO thin films with broccoli-like structure were prepared using a facile hydrothermal method to construct photocathodes for water-splitting application. The morphological, structural, and optical properties of thin films were characterized and measur...
Splitting methods provide an efficient approach to solving evolutionary wave equations, especially in situations where dispersive and nonlinear effects on wave propagation can be separated, as in the generalized nonlinear Schrödinger equation (G...
In this paper, we obtain a new equivalent fixed-point form of the linear complementarity problem by introducing a relaxed matrix and establish a class of relaxed modulus-based matrix splitting iteration methods for solving the linear complementarity...
We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-d...
The tensor absolute value equation is a class of interesting structured multilinear systems. In this article, from the perspective of pure numerical algebra, we first consider a tensor-type successive over-relaxation method (SOR) (called TSOR) and te...
In this paper, we study a split-step Galerkin finite element (FE) method for the two-dimensional Riesz space-fractional coupled nonlinear Schrödinger equations (CNLSs). The proposed method adopts a second-order split-step technique to handle the...
In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the s...
When radar receivers adopt digital channelization, it is prone to generating a cross-channel split signal, the rabbit ear effect, and a transition band repeated signal, leading to errors in radar signal sorting or identification. The pulse-splitting...
In this paper, the original
The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrari...
The purpose of this paper is to find a common element of the fixed point set of a nonexpansive mapping and the set of solutions of the general split variational inclusion problem in symmetric Hilbert spaces by using the inertial viscosity iterative m...
We designed a modified projection method with a new condition of the inertial step and the step size for the split feasibility problem in Hilbert spaces. We show that our iterate weakly converged to a solution. Lastly, we give numerical examples and...
We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and...
Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple o...
Research on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated co...
We introduce two approaches by modifying split-step exponential schemes to study stochastic differential equations. Under the Lipschitz condition and linear-growth bounds, it is shown that our explicit schemes converge to the solution of the correspo...
Geometric image transformations are fundamental to image processing, computer vision and graphics, with critical applications to pattern recognition and facial identification. The splitting-integrating method (SIM) is well suited to the inverse trans...
This study focuses on analyzing the almost sure exponential stability of the split-step
Novel energy generation technologies, such as high-permeability wind power and photovoltaic systems, exhibit inherent intermittency, randomness, and volatility. During periods of energy production from these sources, the impedance of the electrical g...
The split feasibility problem (SFP) has many practical applications, which has attracted the attention of many authors. In this paper, we propose a different method to solve the SFP and the fixed-point problem involving quasi-nonexpansive mappings. W...
In this paper, we propose an inertial parametric Douglas–Rachford splitting method for minimizing the sum of two nonconvex functions, which has a wide range of applications. The proposed algorithm combines the inertial technique, the parametric...
The understanding of the structure of knowledge is an essential step of education. Although teachers offer the information foundation and relationship among knowledge points, there are still few methods to encourage students to explore the structure...
The Split Bregman method (SBM), a popular and universal CS reconstruction algorithm for inverse problems with both l1-norm and TV-norm regularization, has been extensively applied in complex domains through the complex-to-real transforming technique,...
In this paper, a new multi-parameter iterative algorithm is proposed to address the PageRank problem based on the multi-splitting iteration method. The proposed method solves two linear subsystems at each iteration by splitting the coefficient matrix...
In this article, we study a directed version of Douglas–Rachford splitting method in real Hilbert spaces. By using new, self-contained, and simplified techniques, we prove its weak convergence. The major innovation is that we exploit the firm n...
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