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...
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...
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...
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...
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...
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...
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...
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...
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...
In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and the Caputo derivative in the application of the Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze fractional n...
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
There has been considerable interest in seeking exact solutions of non-linear evolution equations that describe important physical and biological processes. Nonetheless, it is a difficult undertaking to determine closed form solutions of mathematical...
A new numerical method for solving Volterra non-linear convolution integral equations (NLCVIEs) of the second kind is presented in this work. This new approach, named IIRFM-A, is based on the combined use of the Laplace transformation, a first-order...
A stochastic material point method is proposed for stochastic analysis in non-linear dynamics of metals with varying random material properties. The basic random variables are parameters of equation of state and those of constitutive equation. In con...
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...
In this paper, we use the averaging method to find an approximate solution for the optimal control of non-linear differential inclusions with fast-oscillating coefficients on a finite time interval.
This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville’s fractional integral and the Caputo derivative. This approach elim...
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...
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...
This study uses an optimization approach representation and numerical solution for the variable viscosity and non-linear Boussinesq effects on the free convection over a vertical truncated cone in porous media. The surface of the vertical truncated c...
We propose a new optimal iterative scheme without memory free from derivatives for solving non-linear equations. There are many iterative schemes existing in the literature which either diverge or fail to work when
This paper presents a method of extracting temperature-dependent parameters of thermoelectric material from the operating conditions of thermoelectric cooler (TEC). Based on the finite element method of calculating TEC’s performance, non-linear...
Until now, there have been no published attempts to utilize ensemble learning approaches to pre-crash velocity estimation. In this research article, we focus on the method of vehicle crash velocity prediction based on the random forest regression app...
Vibration-control techniques generally fall into two categories: passive methods that optimize the structure of the suspension to absorb any impact from the ground, and active methods that directly control the vertical force of the suspension by hydr...
In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from...
A few literary scholars have long claimed that Shakespeare did not write some of his best plays (history plays and tragedies) and proposed at one time or another various suspect authorship candidates. Most modern-day scholars of Shakespeare have reje...
Understanding human cortical neurodynamics is increasingly important, as highlighted by the European Innovation Council, which prioritises tools for measuring and stimulating brain activity. Unravelling how cytoarchitecture, morphology, and connectiv...
This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an op...
In this work, we study the existence and uniqueness of the solution to a wave equation with dynamic Wentztell-type boundary conditions on a part of the boundary
Dynamic analyses of vertical hydro power plant rotors require the consideration of the non-linear bearing characteristics. This study investigates the vibrational behavior of a typical vertical machine using a time integration method that considers n...
Background/Objectives: Cancer is a dynamic and complex disease that remains largely untreated despite major advances in oncology and treatment. In this context, we aimed here to investigate optimal control techniques in the management of tumor growth...
Studying the characteristics of materials through a finite element analysis (FEA) has various benefits; hence, many studies have been conducted to improve the reliability of the analysis results. In general, the mechanical properties used in FEA for...
This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (...
Most complex physical phenomena are described by non-linear Burgers’ equations, which help us understand them better. This article uses the transformation and the fractional Taylor’s formula to find approximate solutions for non-linear fr...
Linear dependence of variables is a commonly used assumption in most diagnostic systems for which many robust methodologies have been developed over the years. In case the system nonlinearities are relevant, fault diagnosis methods, relying on the as...
This paper provides a recent overview of the exact, approximate, and hybrid optimization methods that handle Multi-Objective Mixed-Integer Non-Linear Programming (MO-MINLP) problems. Both the domains of exact and approximate research have experienced...
High-performance liquid chromatography (HPLC) is a dynamic separation process with a lot of parameters having different roles. The equilibrium-dispersive model is relevant for simulating HPLC because it is relatively simple and suitable for high-effi...
In this article, we propose a modified self-adaptive conjugate gradient algorithm for handling nonlinear monotone equations with the constraints being convex. Under some nice conditions, the global convergence of the method was established. Numerical...
Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with...
Wheat quality assessment involves physical, physicochemical, chemical, and sensory characterization of wheat kernels and the resulting wheat flour, dough, and bread. The physical tests conducted on wheat flour dough are mostly based on empirical meth...
The KdV equation has special significance as it describes various physical phenomena. In this paper, we use two methods, namely, a variational homotopy perturbation method and a classical finite-difference method, to solve 1D and 2D KdV equations wit...
In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der P...
This paper evaluates the practice of using moment connections in the perimeter of the structural system and shear connections within the interior connections of the three-dimensional structural system from the perspective of resistance to progressive...
The present exploration discusses the combined effect of non-linear thermal radiation along with viscous dissipation and magnetic field through a porous medium. A distinctive aspect of our work is the simultaneous use of porous wall and a porous mate...
In this article, we use the homotopy perturbation transform method to find the fractional Kersten–Krasil’shchik coupled Korteweg–de Vries (KdV) non-linear system. This coupled non-linear system is typically used to describe electric circuits, traffic...
The solution of the non-linear Föppl–von Kármán equations for square plates in the form of expansion over a system of eigenfunctions, generated by a linear self-adjoint operator, is obtained. The coefficients of the expansion...
The article studies the simulation-based mathematical modeling of bioheat transfer under the Dirichlet boundary condition. We used complex non-linear dual-phase-lag bioheat transfer (DPLBHT) for analyzing the temperature distribution in skin tissues...
This paper aims to use non-linear physical analysis to calculate the displacement of beams and slabs in a cracked state. This study uses the commercial software SAP2000 to perform a numerical analysis using the finite element formulation, applying th...
The present study concerns investigating the two-dimensional Magnetohydrodynamics (MHD) boundary layer flow of Williamson nanofluid over a non-linear stretching sheet. The focus of this study is based on the global influence of the non-Newtonian Will...
We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugg...
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