Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing bu...
In this paper, an efficient decomposition method is constructed and used for solving system of nonlinear equations. The method based on the decomposition technique of Noor [M.A.Noor, K.I.Noor, Some iterative schemes for nonlinear equations, Appl. Mat...
This paper presents an unconditionally stable integration method, which introduces a linearly implicit algorithm featuring an explicit displacement expression. The technique that is being considered integrates one Newton iteration into the mean accel...
In this paper, we developed a new variational iteration method using the quasilinearization method and Adomian polynomial to solve nonlinear differential equations. The convergence analysis of our new method is also discussed under the Lipschitz cont...
In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described...
Regression analysis is widely applied in many fields of science to estimate important variables. In general, nonlinear regression is a complex optimization problem and presents intrinsic difficulties in estimating reliable parameters. Nonlinear optim...
In this work, the analytical derivation and the computer implementation of the adjoint method are described. The adjoint method can be effectively used for solving the optimal control problem associated with a large class of nonlinear mechanical syst...
Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology...
In this study, a collocation method based on Bernstein polynomials is developed for solution of the nonlinear ordinary differential equations with variable coefficients, under the mixed conditions. These equations are expressed as linear ordinary dif...
Traub’s method was extended here to systems of nonlinear equations and compared to Steffensen’s method. Even though Traub’s method is only of order 1.839 and not quadratic, it performed better in the 10 examples.
In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomia...
In this study, an efficient localized method of fundamental solution (LMFS) is applied to nonlinear heat conduction with mixed boundary conditions. Since the thermal conductivity is temperature-dependent, the Kirchhoff transformation is used to trans...
A compensation method for nonlinear vibration of a silicon micro resonant sensor is proposed and evaluated to be effective through simulation and experimental analysis. Firstly, the parameter characterization model of the silicon micro resonant senso...
An explicit method for solving time fractional wave equations with various nonlinearity is proposed using techniques of Laplace transform and wavelet approximation of functions and their integrals. To construct this method, a generalized Coiflet with...
We have proposed a development of the variational iteration method (VIM), or extended Kantorovich method, by studying physically nonlinear (FN) or geometrically nonlinear (GN) Kirchhoff nanoplates as an example. The modified couple stress theory was...
In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary cond...
Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate soluti...
Tube/Pipe (TP) 304 stainless steel has been widely used in industry, but a change in its microstructures may endanger its service safety, and it is essential to evaluate its microstructural evolution. In this work, a pulse-echo nonlinear method is pr...
In this paper, we present a new sixth-order iterative method for solving nonlinear systems and prove a local convergence result. The new method requires solving five linear systems per iteration. An important feature of the new method is that the LU...
A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated. It is also shown that the method has much fewer divergent p...
This paper presents a co-rotational beam formulation, which is used for geometric nonlinear analysis with the differential reproducing kernel (DRK) approximation collocation method. The present formulation, based on the Timoshenko beam hypothesis, is...
Based on the direct differentiation method, sensitivity analysis of transient responses with respect to local nonlinearity is developed in this paper. Solutions of nonlinear equations and time-domain integration are combined to compute the response s...
The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hiro...
In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem...
There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are “small” compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Metho...
With increasing demands for huge ship dimensions and the wide use of high-strength steel, the influence of slamming and elastic structure on structural strength cannot be ignored. Therefore, in this paper, a three-dimensional (3D) nonlinear hydroelas...
In light of the complex behavior of vibrating structures, their reliable modeling plays a crucial role in the analysis and system design for vibration control. In this paper, the reverse-path (RP) method is revisited, further developed, and applied t...
One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations....
In this work, we integrate some new approximate functions using the logarithmic penalty method to solve nonlinear optimization problems. Firstly, we determine the direction by Newton’s method. Then, we establish an efficient algorithm to comput...
In this paper, a meshfree weighted radial basis collocation method associated with the Newton’s iteration method is introduced to solve the nonlinear inverse Helmholtz problems for identifying the parameter. All the measurement data can be incl...
A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant paramete...
A recently developed perturbation algorithm namely the multiple scales Lindstedt-Poincare method (MSLP) is employed to solve the mathematical models. Three different models with quadratic nonlinearities are considered. Approximate solutions are obt...
We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by approximat...
This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi polynomial method (GPM). We have provided proof to demonstrate the existence of a unique solution to the second sort of NFrIE in Hilbert space. The proof of the...
In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an...
The objective of this study is to explore a noble application of the improved homotopy perturbation procedure bases in structural engineering by applying it to the geometrically nonlinear analysis of the space trusses. The improved perturbation algor...
We adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform...
In our paper, we present a sparse quasi-Newton method, called the sparse direct Broyden method, for solving sparse nonlinear equations. The method can be seen as a Broyden-like method and is a least change update satisfying the sparsity condition and...
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...
A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low...
A generalized Krylov-Bogoliubov-Mitropolsky (KBM) method is extended for the study of strongly nonlinear oscillators with slowly varying parameters. The asymptotic amplitude and phase are derived and then the asymptotic solutions of arbitrary order a...
This paper presents a meshless Galerkin method for analyzing the nonlinear behavior of corrugated sandwich plates. A corrugated sandwich plate is a composite structure comprising two flat face sheets and a corrugated core, which can be approximated a...
This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first gene...
In this work, we study a numerical method to approximate the exact solution of a simple in situ combustion model. To achieve this, we use the mixed nonlinear complementarity method (MNCP), a variation of the Newton method for solving nonlinear system...
The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method...
As the strength parameters of rock mass degrade differently during slope instability, different factors should be considered in the strength reduction method. Previous nonlinear reduction methods were essentially implemented based on the Mohr–C...
Navigation grade inertial measurement units (IMUs) should be calibrated after Inertial Navigation Systems (INSs) are assembled and be re-calibrated after certain periods of time. The multi-position calibration methods with advantage of not requiring...
A solution of a nonlinear perturbed unconstrained point-to-point control problem, in which the unperturbed system is differentially flat, is considered in the paper. An admissible open-loop control in it is constructed using the covering method. The...
In this paper, we propose an efficient numerical method for solving an initial boundary value problem for a coupled system of equations consisting of a nonlinear parabolic partial integro-differential equation and an elliptic equation with a nonlinea...
This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal d...
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