The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree
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...
We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propo...
The Gauss–Newton–Broyden method is proposed and investigated for solving a nonlinear least squares problem with operator decomposition. This method is obtained from the Gauss–Newton method by replacing the Jacobian matrix of a nonli...
In this paper, we propose a new version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems based on the transformation to the nonsmooth equation, which is equivalent to some unconstrained optimization p...
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to find Lie...
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 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...
To solve linear and nonlinear eigenvalue problems, we develop a simple method by directly solving a nonhomogeneous system obtained by supplementing a normalization condition on the eigen-equation for the uniqueness of the eigenvector. The novelty of...
The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the l...
In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of first order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocat...
In this paper, we focus on the existence of solutions of the nonlinear Langevin fractional differential equations involving anti-periodic boundary value conditions. By using some techniques, formulas of solutions for the above problem and some proper...
We study a boundary value problem for nonlinear partial differential equations of the hyperbolic type on the plain in a domain with a complex boundary. To find the missing data for the given boundary constraints, we solve a supplementary nonlinear pr...
An algorithm based on the human evolutionary model is proposed for solving nonlinear bilevel programing problems. In view of the hierarchical structure of this problem, the algorithm is designed through feeding back the optimal solution of the lower-...
We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regul...
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...
In this paper, by using the smoothing Fischer-Burmeister function, we present a new smoothing conjugate gradient method for solving the nonlinear nonsmooth complementarity problems. The line search which we used guarantees the descent of the method....
In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter
In this paper, we explore specific fixed-point outcomes under a Mukherjea-Type nonlinear description of almost contractions in a metric space with a locally ℏ-transitive binary relation. Numerous previous insights are expanded, developed, impro...
In this paper, an efficient computational discretization approach is investigated for nonlinear fourth-order boundary value problems using beam theory. We specifically deal with nonlinear models described by fourth-order boundary value problems. The...
The paper presents the Generalized Benders Decomposition (GBD) method, which is now one of the basic approaches to solve big mixed-integer nonlinear optimization problems. It concentrates on the basic formulation with convex objectives and constraint...
We prove the logarithmic convergence rate of the families of usual and modified iterative Runge-Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results....
In this paper, we deal with the properties and applications of a nonlinear scalarization function for sets by using the Minkowski difference. Under some suitable assumptions, the continuity and convexity concerned with the nonlinear scalarization fun...
In the numerical integration of the second-order nonlinear boundary value problem (BVP), the right boundary condition plays the role as a target equation, which is solved either by the half-interval method (HIM) or a new derivative-free Newton method...
Inverse heat transfer problems are important in numerous scientific research and engineering applications. This paper proposes a network-based method utilizing the nonlinear autoregressive with exogenous inputs (NARX) neural network, which can achiev...
The connectedness and path connectedness of the solution sets to vector optimization problems is an important and interesting study in optimization theories and applications. Most papers involving the direction established the connectedness and conne...
We study an iterative differential-difference method for solving nonlinear least squares problems, which uses, instead of the Jacobian, the sum of derivative of differentiable parts of operator and divided difference of nondifferentiable parts. Moreo...
To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differenti...
We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and deter...
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...
Job shop scheduling problem (JSSP) has high theoretical and practical significance in academia and manufacturing respectively. Therefore, scholars in many different fields have been attracted to study this problem, and many meta-heuristic algorithms...
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...
Iterative methods for solving constraint nonlinear monotone equations have been developed and improved by many researchers. The aim of this research is to present a modified three-term conjugate descent (TTCD) derivative-free method for constrained n...
In this paper, we study a class of fractional nonlinear second order Volterra integro-differential type of singularly perturbed problems with fractional order. We divide the problem into two subproblems. The first subproblems is the reduced problem w...
A variety of methods that provide approximate piecewise- analytical solutions to initial-value problems governed by scalar, nonlinear, first-order, ordinary differential equations is presented. The methods are based on fixing the independent variable...
A spherically constrained nonlinear eigenvalue problem (NEPv) arising in Bose–Einstein condensates (BEC) is investigated. The Projected Gradient Method (PGM) is proposed and analyzed in detail. Rigorous theoretical analysis establishes its glob...
In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier K...
Piecewise analytical solutions to scalar, nonlinear, first-order, ordinary differential equations based on the second-order Taylor series expansion of their right-hand sides that result in Riccati’s equations are presented. Closed-form solution...
A wavelet transform twofold subspace-based optimization method (WT-TSOM) is proposed to solve the highly nonlinear inverse scattering problems with contraction integral equation for inversion (CIE-I). While the CIE-I is able to suppress the multiple...
In this study, a novel application of neurocomputing technique is presented for solving nonlinear heat transfer and natural convection porous fin problems arising in almost all areas of engineering and technology, especially in mechanical engineering...
In this paper, we investigate the existence of an absolute continuous solution to a class of first-order nonlinear differential equation with integral boundary conditions (BCs) or with infinite-point BCs. The Liouville-Caputo fractional derivative is...
This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed...
In this paper, we consider a direct problem and an inverse problem involving a nonlinear fractional diffusion equation, which can be applied to many physical situations. The equation contains a Caputo fractional derivative, a symmetric uniformly elli...
Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it’s necessary to simultaneously optimize a number of non-linear an...
This paper investigates a nonlinear Bitsadze–Samarskii type boundary value problem for an elliptic-hyperbolic operator. First, we establish necessary and sufficient conditions for the unique solvability of the corresponding linear mixed-type pr...
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...
Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is non...
This work presents a procedure for constructing the solution of a second order nonlinear partial differential equation subjected to nonlinear boundary conditions in a very simple and systematic way. The class of equations to be considered here includ...
This paper investigates the solution for an inverse of a parametric nonlinear transportation problem, in which, for a certain values of the parameters, the cost of the unit transportation in the basic problem are adapted as little as possible so that...
The paper focuses on the problem of a monochromatic terahertz TE-polarized wave propagation in a plane dielectric layer filled with a homogeneous isotropic medium; one of the boundaries of the waveguide is covered with a layer of graphene. In fact, t...
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