In this paper, we rst prove a convergence result on the Ka canov method for solving general nonlinear variational inequalities of the second kind. Then we apply the Ka canov method to solve a nonlinear variational inequality of the second kind arising in elastoplasticity. In addition to the convergence result, we show an a posteriori error estimate for the Ka canov iterates. In each step of the...

Variational iteration method VIM is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iterat...

In this paper, we introduce and analyze a hybrid steepest-descent extragradient algorithm for solving triple hierarchical pseudomonotone variational inequalities in a real Hilbert space. The proposed algorithm is based on Korpelevich’s extragradient method, Mann’s iteration method, hybrid steepest-descent method and Halpern’s iteration method. Under mild conditions, the strong convergence of th...

In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of the sequence become complicated, and therefore, computing a highly accurate solution would be difficult or even impossible. In this paper, for one-dimensional...

In this paper, we apply the variational iteration method using He’s polynomials for finding the analytical solution of gas dynamic equation. The proposed method is an elegant combination of He’s variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the s...

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.