In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation AXB = C has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficien...

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...

DIME is a programming environment for manipulation of irregular triangular meshes with a distributed memory machine. We have added a software layer DIMEFEM which manipulates Finite Element representations of functions and allows the stating and solving of variational statements. An application of DIMEFEM is an incompressible Navier-Stokes solver with a three-stage implicit time step, using quas...

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...