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 boundary layer micropolar fluid over a horizontal plate embedded in a non-Darcy porous medium is investigated in this study. This paper is solely focused on contributions oriented towards the application of micropolar fluid flow over a stretching...
In this paper, we consider a class of structured optimization problems whose objective function is the summation of two convex functions: f and h, which are not necessarily differentiable. We focus particularly on the case where the function f is gen...
Currently, the tasks of intelligent data analysis in medicine are becoming increasingly common. Existing artificial intelligence tools provide high effectiveness in solving these tasks when analyzing sufficiently large datasets. However, when there i...
The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting poi...
Inerter-based dampers have gained great popularity in structural vibration control. In this paper, equivalent linearization methods (ELMs) for a single-degree-of-freedom (SDOF) system with a clutching inerter damper (CID) are studied. The comparison...
In this paper, we present a comparative study between Sinc–Galerkin method and a modified version of the variational iteration method (VIM) to solve non-linear Sturm–Liouville eigenvalue problem. In the Sinc method, the problem under cons...
A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman–Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was fi...
Block hybrid methods with intra-step points are considered in this study. These methods are implemented to solve linear and nonlinear single and systems of first order differential equations. The stability, convergence, and accuracy of the proposed m...
In the paper, two new analytic methods using the decomposition and linearization technique on nonlinear differential/integral equations are developed, namely, the decomposition–linearization–sequential method (DLSM) and the linearized hom...
Accurate assessment and prediction of mandible shape are fundamental prerequisites for successful orthognathic surgery. Previous studies have predominantly used linear models to predict lower facial structures from facial landmarks or measurements; t...
We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropr...
The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy...
This paper presents an extended comparison study between 16 different linear and non-linear regression methods to predict the sugar, pH, and anthocyanin contents of grapes through hyperspectral imaging (HIS). Despite the numerous studies on this subj...
In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalu...
Influences of angular misalignments of a small cylinder on its roundness measurement by the method referred to as the stitching linear scan method are theoretically investigated. To compensate for the influences, a technique for measuring angular mis...
Food analysis is a challenging analytical problem, often addressed using sophisticated laboratory methods that produce large data sets. Linear and non-linear multivariate methods can be used to process these types of datasets and to answer questions...
Ride-hailing services have grown rapidly, presenting challenges such as increased traffic congestion, inefficient driver workload distribution, and environmental concerns like higher fuel consumption and emissions. This study develops a non-linear ri...
Sequential linear models can be adopted to describe the data where the response variable depends on lagged outcomes and fixed-effects variables. For estimation, variable selection, and high-accuracy response prediction, we propose the penalized metho...
Efficient and accurate time integration is essential for simulating combustion processes with stiff, multiscale dynamics arising from diffusion, reaction, and advection interactions. Standard implicit–explicit (IMEX) methods employ a two-additi...
In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of...
In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data....
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...
An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing a...
The aim of this article is to investigate the parameter sensitivity of the (Non-Linear) Unsteady Vortex Lattice Method-Vortex Particle Method [(NL-)UVLM-VPM] with Particle Strength Exchange-Large Eddy Simulations (PSE-LES) method on a lower Reynolds...
Approximation of piecewise linear and generalized functions is an important and difficult problem. These functions are widely used in mathematical modeling of various processes and systems, such as: automatic control theory, electrical engineering, r...
The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems. However,...
The boundary shape function method (BSFM) and the variational iteration method (VIM) are merged together to seek the analytic solutions of nonlinear boundary value problems. The boundary shape function method transforms the boundary value problem to...
This work deals with switching structured linear systems, a class of structured linear systems whose existing links between the state, input, and output variables have unknown numerical values and, in addition, are subject to change according to an e...
A numerical study was performed to investigate the applicability of the linear decomposition method for the hydrodynamic energy conversion of an oscillating-water-column type wave energy converter (OWC-WEC). Hydrodynamic problems of the OWC chamber w...
Subgradient methods are frequently used for optimization problems. However, subgradient techniques are characterized by slow convergence for minimizing ravine convex functions. To accelerate subgradient methods, special linear non-orthogonal transfor...
In this study, analysis of core-loss occurring in the magnetic flux modulation core of a linear magnetic gear and the core of each mover is presented, using an analytical method. Losses in electric machines were generally calculated and analyzed usin...
The Electrostatic Discharge phenomenon is a great threat to all electronic devices and ICs. An electric charge passing rapidly from a charged body to another can seriously harm the last one. However, there is a lack in a linear mathematical approach...
The iterative decreasing dimension method (IDDM) is an iterative method used to solve the linear algebraic system
Regularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and p...
This paper proposes an outer space branch-and-search method for a class of linear fractional programming problems over a polytope. First, the original problem is reformulated in an equivalent problem by applying the equivalent transformation. Second,...
In 2013, Bai and Zhang constructed modulus-based synchronous multisplitting methods for linear complementarity problems and analyzed the corresponding convergence. In 2014, Zhang and Li studied the weaker convergence results based on linear complemen...
Linear ultrasonic motors can output large thrust stably in a narrow space. In this paper, a plate linear ultrasonic motor is studied. Firstly, the configuration and operating principle of the
In this paper, a two-step iteration method was established which can be viewed as a generalisation of the existing modulus-based methods for vertical linear complementarity problems. The convergence analysis of the proposed method is presented, which...
This paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces...
A new two-step interior point method for solving linear programs is presented. The technique uses a convex combination of the auxiliary and central points to compute the search direction. To update the central point, we find the best value for step s...
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...
In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ansätz. The improved method has two advantages. One is that it can solve non-linear lattice equation...
A direct linear plot was applied to estimate kinetic constants using the product’s competitive inhibition equation. The challenge consisted of estimating three kinetic constants, Vmax, Km, and Kp, using two independent variables, substrates, an...
Attempts are made in this paper to improve the quality of the stitching between adjacent arc-profiles in the stitching linear-scan method for the roundness measurement of a cylinder in a small dimension. The data in the edge region of an arc-profile,...
The most popular iterative methods for solving nonsymmetric linear systems are Krylov methods. Recently, an optimal Quasi-ORthogonal (Q-OR) method was introduced, which yields the same residual norms as the Generalized Minimum Residual (GMRES) method...
This study presents a hybrid non-linear unsteady vortex lattice method-vortex particle method (NL UVLM-VPM) to investigate the aerodynamics of rotor blades hovering in and out of ground effect. The method is of interest for the fast aerodynamic predi...
Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which results in fuzzy parameters rather than crisp parameters....
A new frequency–amplitude formula by improving an ancient Chinese mathematics method results in a modification of He’s formula. The Chinese mathematics method that expresses via a fixed-point Newton form is proven to be equivalent to the...
Panel-based aeroelasticity models are commonly used to conduct mid-fidelity aeroelastic analysis. The unsteady vortex lattice method (UVLM) in particular is used when non-linear aerodynamic corrections are needed, for example by utilizing the
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