In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the prop...
This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid...
The present paper makes use of the efficient double decomposition method to propose a method for solving two-point boundary-value problems, featuring second- and higher-order nonlinear ordinary differential equations. The efficacy of the proposed met...
This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subseq...
In this paper, a new approximate method for solving higher-order linear ordinary differential equations with variable coefficients under the mixed conditions is presented. The method is based on the rational Chebyshev (RC) Tau, Chebyshev and Taylor c...
This study introduces the higher-order unconditionally positive finite difference (HUPFD) methods to solve the linear, nonlinear, and system of advection–diffusion–reaction (ADR) equations. The stability and consistency of the developed m...
We propose higher-order adaptive energy-preserving methods for a charged particle system and a guiding center system. The higher-order energy-preserving methods are symmetric and are constructed by composing the second-order energy-preserving methods...
High-density polyethylene (HDPE) pipes are becoming increasingly popular, being used in various fields, such as construction, marine, petroleum, water transfer, process water, methane gas collection, oil and gas gathering, gas distribution systems, m...
The conventional approach of the local convergence analysis of an iterative method on Rm, with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives...
The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations....
Multi-modal fusion can achieve better predictions through the amalgamation of information from different modalities. To improve the performance of accuracy, a method based on Higher-order Orthogonal Iteration Decomposition and Projection (HOIDP) is p...
An unsteady formulation of the Kutta–Joukowski theorem has been used with a higher-order potential flow method for the prediction of three-dimensional unsteady lift. This study describes the implementation and verification of the approach in de...
Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method gen...
Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representin...
We consider an inverse spectral problem that consists in the recovery of the differential expression coefficients for higher-order operators with separate boundary conditions from the spectral data (eigenvalues and weight numbers). This paper is focu...
Traditional data-driven soft sensor methods can be regarded as an optimization process to minimize the predicted error. When applying the mean squared error as the objective function, the model tends to be trained to minimize the global errors of ove...
In this article, a new higher-order convergence Laplace–Fourier method is developed to obtain the solutions of linear neutral delay differential equations. The proposed method provides more accurate solutions than the ones provided by the pure...
The cubature Kalman filter (CKF) cannot accurately estimate the nonlinear model, and these errors will have an impact on the accuracy. In order to improve the filtering performance of the CKF, this paper proposes a new CKF method to improve the estim...
The order reduction method is an important approach to optimize higher-order binary Markov random fields (HoMRFs), which are widely used in information theory, machine learning and image analysis. It transforms an HoMRF into an equivalent and easier...
A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechan...
The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defin...
A very fast reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real time, by using synthetic data collected in specific sensors. This reduced model is constructed by applying higher...
In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional derivatives (Caputo and Riemann–Liouville) and conformable derivatives. It has also been...
The traditional single-mode fiber (SMF) optical time domain reflectometer (OTDR) may not be able to accurately detect and locate fault events in the dead zone of few-mode fiber (FMF) links. This paper introduces the concept of higher-order spatial mo...
The finite element method (FEM) is widely used in many engineering applications. The popularity of FEM led to the development of several variants of formulations, and hexahedral meshes surged as one of the most computationally effective. After briefl...
An ultrasonic reverse time migration imaging method, based on high-order singular value decomposition, is proposed in the study to solve the problems of low signal-to-noise ratio (SNR) and excessive artifacts in defect ultrasonic detection imaging re...
Here we propose an online method to explore the multiway nature of urban spaces data for outlier detection based on higher-order singular value tensor decomposition. Our proposal has two sequential steps: (i) the offline modeling step, where we model...
A high-speed advancing ship will cause significant squats in shallow water, which could increase the risk of grounding. To this end, a program based on the Rankine higher-order boundary element method (HOBEM) is developed to investigate a high-speed...
Most electrical machines and drive signals are non-Gaussian and are highly nonlinear in nature. A useful set of techniques to examine such signals relies on higher-order statistics (HOS) spectral representations. They describe statistical dependencie...
The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is...
Nonlinear transverse free vibrations of porous functionally-graded (FG) Bernoulli–Euler nanobeams in hygrothermal environments through the local/nonlocal stress gradient theory of elasticity were studied. By using the Galerkin method, the gover...
The study of heat transfer deals with the determination of the rate of heat energy transfer from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often the fundamental principle behind severa...
Three new iterative methods for solving scalar nonlinear equations using weight function technique are presented. The first one is a two-step fifth order method with four function evaluations which is improved from a two-step Newton’s method ha...
In this contribution, the variational problem for the Kirchhoff plate based on the modified strain gradient theory (MSGT) is derived, and the Euler-Lagrange equations governing the equation of motion are obtained. The Galerkin-type weak form, upon wh...
The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by...
In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. I...
This paper presents an efficient framework for estimating the direction-of-arrival (DOA) of wideband sound sources. The proposed framework provides an efficient way to construct a wideband cross-correlation matrix from multiple narrowband cross-corre...
The Finite Element Method (FEM) has emerged as a powerful tool for predicting the behavior of industrial products, including those with complex geometries or uncommon materials. Finite Element Analysis (FEA) is widely used to study structural vibrati...
The Akhmediev breather (AB) solution of the nonlinear Schrödinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution. Several fully...
The proliferation of renewable energy sources and distributed generation systems interfaced to the grid by power electronics systems is forcing us to better understand the issues arising due to the quality of electrical signals generated through thes...
Offshore wind turbines serve as critical infrastructure components in marine renewable energy systems, enabling sustainable energy extraction within offshore engineering frameworks. Monopile foundations for offshore wind turbines in deep-water enviro...
The uncertainty caused by renewable energy (RES) and diverse load demands may cause power flow fluctuations in modern power systems, where the probabilistic power flow (PPF) is a reliable method for quantifying and analyzing such power flow fluctuati...
Presented herein is the free vibration analysis of functionally graded beams (FGMs) via higher-order shear deformation theory and an artificial neural network method (ANN). The transverse displacement (w) is expressed as bending (wb) and shear (ws) c...
Space-based optical imaging detection serves as a crucial means for acquiring characteristic information of space objects, with the quality and resolution of images directly influencing the accuracy of subsequent missions. Addressing the scarcity of...
In order to improve the understanding of hydrodynamic performances of spar-type Floating Offshore Wind Turbines (FOWTs), in particular the effect of wave-current-structure interaction, a moored 6MW spar-type FOWT in regular waves and uniform current...
Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) wit...
The paper is devoted to the parametric stability optimization of explicit Runge–Kutta methods with higher-order derivatives. The key feature of these methods is the dependence of the coefficients of their stability polynomials on free parameter...
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs) was originally formulated using Euler time discretizations and a uniform space grid. In this paper, we utilize a tree-like spatial discre...
The lasso and elastic net methods are the popular technique for parameter estimation and variable selection. Moreover, the adaptive lasso and elastic net methods use the adaptive weights on the penalty function based on the lasso and elastic net esti...
A new family of iterative methods for solving systems of nonlinear equations is introduced, extending and unifying several existing approaches within a general framework. In the single-variable case, Newton’s method was accelerated using Pad&ea...
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