In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...

The aim of this paper is to present the recently proposed fluid diffusion based algorithm in the general context of the matrix inversion problem associated to the Gauss-Seidel method. We explain the simple intuitions that are behind this diffusion method and how it can outperform existing methods. Then we present some theoretical problems that are associated to this representation as open resea...

During the sixties, the notion of 2-metric space introduced by Gähler see 1, 2 as a generalization of usual notion ofmetric space X, d . But different authors proved that there is no relation between these two functions, for instance, Ha et al. in 3 show that 2-metric need not be continuous function, further there is no easy relationship between results obtained in the two settings. In 1992, Ba...

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu+ u = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method. Keywords—Positive Solutions; Newton’s Method; Contractor Iteration Method; Eigenpairs.

AbstractAn analytic technique, combination of two methods Homotopy Perturbation Method and Variational Iteration Method are applied for solve second kind of linear Volteera equations. homotopy perturbation method and variational iteration method are employed to solve Volteera integral equations. The result reveals that the homotopy perturbation method and variational iteration method are very e...

We present a new hybrid algorithm based on Godunov’s method for computing eigenvectors of symmetric tridiagonal matrices and Inverse Iteration, which we call the Godunov–Inverse Iteration. We use eigenvectors computed according to Godunov’s method as starting vectors in the Inverse Iteration, replacing any nonnumeric elements of Godunov’s eigenvectors with random uniform numbers. We use the rig...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Thr...

Let {ak}, k = 1, . . . , N be a family of matrices of sizes rk × rk−1. For positive integers i, j, i > j define the operation aij as follows: a × ij = ai−1 · · ·aj+1 for i > j + 1, aj+1,j = Irj . Let {bk}, k = 1, . . . , N be a family of matrices of sizes rk−1 × rk. For positive integers i, j, j > i define the operation bij as follows: b × ij = bi+1 · · · bj−1 for j > i+ 1, bi,i+1 = Iri . It is...