We prove that, under certain conditions, some classical iterative methods converge for the linear system resulting from a fourth-order compact discretization of the convection-diiusion equation.

E. Azadegan , R. Ezzati Department of Mathematics, Islamic Azad University-Karaj Branch, Karaj, Iran |||||||||||||||||||||||||||||||Abstract In this paper, we present a new two-parameters family of iterative methods for solving non-linear equations and prove that the order of convergence of these methods is at least four. Per iteration of these new methods require two evaluations of the functio...

in this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. some new positive periodic criteria are given.

The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used to obtain the same kind of information as from the parameter space, and even more, in complex dynamics.

In this paper we consider a fourth order differential equation with nonlinear boundary condition. The existence and uniqueness of a solution is proved. An iterative method for its solution is proposed and the convergence of the method is established. An interesting property of the sequence of iterative solution in dependence of the monotonicity of the function in nonlinear BC is investigated. N...

Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as circular complex interval arithmetic. The derived iterative formulas are suitable for the construction of modified methods with improved converg...

the goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order  by using ideal. we also investigate certain properties of this convergence.

We study a fourth order finite difference method for the unsteady incompressible Navier-Stokes equations in vorticity formulation. The scheme is essentially compact and can be implemented very efficiently. Either Briley’s formula, or a new higher order formula, which will be derived in this paper, can be chosen as the vorticity boundary condition. By formal Taylor expansion, the new formula for...