In this paper, we apply the modified variational iteration method (MVIM) for solving Schrödinger equations. The proposed modification is made by introducing He’s polynomials in the correction functional of variational iteration method (VIM). The sugg...
The variational iteration method is employed to solve conservative oscillator containing complicated nonlinearities. In order to expand the nonlinear terms into truncated Fourier series, an approach of undetermined coefficient is proposed. Numerical...
Variational iteration method is applied to solve a class of delay differential-algebraic equations. The obtained sequence of iteration is based on the use of Lagrange multipliers. The corresponding convergence results are obtained and successfully co...
In this paper, we use Chebyshev approximations in the process of He’s variational iteration method for finding the solution of differential-algebraic equations. This allows us to make integration at each of the iterations possible and at the same tim...
Multidimensional integro-differential equations are obtained when the unknown function of several independent variable and/or its derivatives appear under an integral sign. When the differentiation or integration operators or both are of fractional o...
In this article, modified techniques, namely the variational iteration transform and Shehu decomposition method, are implemented to achieve an approximate analytical solution for the time-fractional Fornberg–Whitham equation. A comparison is ma...
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, the variational iteration method is proposed to solve system of nonlinear Volterra's integro-differential equations. Four numerical examples are illustrated by this method. The results reveal that this method is very effective and high...
In this paper, the variational iteration method (VIM) is employed to solve a system of fuzzy differential equations of first order. Since every ordinary fuzzy differential equations of higher order can be converted into a fuzzy system of the first or...
This paper presents a modified variational iteration method for solving nonlinear boundary value problems arising in nonlinear oscillatory systems. By introducing dual general Lagrange multipliers, a unified correction functional is constructed for n...
In this paper, we introduced a new generalization method to solve fractional convection–diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in co...
Compared with the linear Black–Scholes model, nonlinear models are constructed through taking account of more practical factors, such as transaction cost, and so it is difficult to find an exact analytical solution. Combining the Haar wavelet integra...
This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexp...
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...
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 the present work, we introduce a hybrid Mann viscosity-like implicit iteration to find solutions of a monotone classical variational inequality with a variational inequality constraint over the common solution set of a general system of variationa...
In this paper, a Burger’s-Fisher equation is solved by using the Adomian’s decomposition method (ADM) , modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotop...
Several iterative integro-differential formulations for two-point, second- and third-order, nonlinear, boundary-value problems of ordinary differential equations based on Green’s functions and the method of variation of parameters are presented...
We formulate an iterative approach employing the inertial technique to approximate the anticipated solution for a generalized mixed variational-like inequality, as well as variational inequality and fixed point problems associated with a relatively n...
In this paper, we propose the new iterative method (NIM) for solving the generalized Burgers–Huxley equation. NIM provides an approximate solution without the need for discretization and is based on a set of iterative equations. We compared the...
In this paper, we introduce a new three-step iterative scheme for finding the common solutions of the variational inequality using the technique of updating the solution. We suggest, iterative algorithms involving three-steps for the predictor-correc...
This study is about the lubrication of a long porous slider in which the fluid is injected into the porous bottom. The similarity transformation reduces the Navier-Stokes equations to couple nonlinear, ordinary differential equations, which are solve...
We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is pi...
In this paper, we examine aspects of general variational inequalities (GVIs) that are similar to fixed-point problems. Special cases of the proposed unique iterative methods are introduced, including the implicit, explicit, and extra-gradient methods...
This work presents an extragradient-type iterative process combined with the viscosity method to find a common solution to a split generalized variational-like inequality, a variational inequality, and a fixed point problem associated with a family o...
In this paper, we consider a new class of variational inequalities which is called the general mixed multivalued nonlinear quasi-variational inequality. We define an iterative algorithm and prove the existence solution for our general mixed multivalu...
In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities...
This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined...
This paper investigates the boundary value in the heat conduction problem by a variational iteration method. Applying the iteration method, a sequence of convergent functions is constructed, the limit approximates the exact solution of the heat condu...
In this study we will check the stability of the semi analytical technique, the Laplace variational iteration (LVI) scheme, which is the combination of a variational iteration technique and the Laplace transform method. Then, we will apply it to solv...
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneou...
In this paper, based on the viscosity approximation method and the hybrid steepest-descent iterative method, a new implicit iterative algorithm is presented for finding the common fixed points set of a finite family of nonexpansive mappings in a refl...
This paper is devoted to studying the existence of solutions to a class of impulsive fractional differential equations with derivative dependence. The used technical approach is based on variational methods and iterative methods. In addition, an exam...
The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM...
The main aim of this research is to introduce and investigate an inertial Tseng iterative method to approximate a common solution for the variational inequality problem for
In this research article, we introduce a novel iterative approach that builds upon a two-step extragradient-viscosity method. This method aims to find a common element among the solution set of a variational inequality, an equilibrium problem, and th...
An option is the right to buy or sell a good at a predetermined price in the future. For customers or financial companies, knowing an option’s pricing is crucial. It is well recognized that the Black–Scholes model is an effective tool for...
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...
In this paper, we study the numerical solution of fractional Jaulent–Miodek equations with the help of two modified methods: coupled fractional variational iteration transformation technique and the Adomian decomposition transformation techniqu...
In this article, the Daftardar-Gejji and Jafari method (DJM) is used to obtain an approximate analytical solution of the sine-Gordon equation. Some examples are solved to demonstrate the accuracy of DJM. A comparison study between DJM, the variationa...
This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique a...
This paper is devoted to the analysis of a system of generalized variational inclusion problems involving
This article extends the celebrated Riemann–Hilbert (RH) method equipped with mixed spectrum to a new integrable system of three-component coupled time-varying coefficient complex mKdV equations (ccmKdVEs for short) generated by the mixed spect...
In this study, two numerical methods—the variational iteration transform method (VITM) and the Adomian decomposition (ADM) method—were used to solve the second- and fourth-order fractional Boussinesq equations. Both methods are helpful in...
Theoretical tire models are often used in tire dynamics analysis and tire design. In the past, scholars have carried out a lot of research on theoretical model modeling; however, little progress has been made on its solution. This paper focuses on th...
In this article, we also introduced two well-known computational techniques for solving the time-fractional Fornberg–Whitham equations. The methods suggested are the modified form of the variational iteration and Adomian decomposition techniques by
In the present paper, the series solutions and the approximate solutions of the time–space fractional differential equations are obtained using two different analytical methods. One is the homotopy perturbation Sumudu transform method (HPSTM), and an...
This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and t...
We present analytical solutions of the Fornberg–Whitham equations with the aid of two well-known methods: Adomian decomposition transform and variational iteration transform involving fractional-order derivatives with the Atangana–Baleanu...
In this research, three numerical methods, namely the variational iteration method, the Adomian decomposition method, and the homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differe...
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