In this paper, we present a new iterative method with order of convergence sixth for solving nonlinear equations. This method is developed by extending a fourth order method of Ostrowski. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the sixth order of convergence is given. Several numerical ex...

In this study by modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we investigate some spectral properties of one Sturm-Liouville type problem on two disjoint intervals.

In this paper we present a new efficient sixth-order scheme for nonlinear equations. The method is compared to severalmembers of the family ofmethods developedbyNeta (1979) [B. Neta, A sixth-order family of methods for nonlinear equations, Int. J. Comput. Math. 7 (1979) 157–161]. It is shown that the newmethod is an improvement over this well known scheme. Published by Elsevier Ltd

How to reduce the horizontal pressure gradient error is a key issue of using s-coordinate ocean models, especially of using primitive equation models for coastal regions. The error is caused by the splitting of the horizontal pressure gradient term into two parts and the subsequent incomplete cancellation of the truncation errors of those parts. Due to the fact that the higher the order of the ...

In this paper, we apply the homotopy perturbation method for solving the sixth-order boundary value problems by reformulating them as an equivalent system of integral equations. This equivalent formulation is obtained by using a suitable transformation. The analytical results of the integral equations have been obtained in terms of convergent series with easily computable components. Several ex...

In this article, we consider the Cauchy problem for sixth-order damped Boussinesq equation in Rn. The well-posedness of global solutions and blow-up of solutions are obtained. The asymptotic behavior of the solution is established by the multiplier method.

A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x 0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performan...

The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see [2]), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cot θ(x) = y′(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful...

We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well known that such problems with Dirichlet boundary conditions can be transformed into an algebraic eigenvalue problem for a banded, real-symmetric matrix, and vice versa. In this article it is shown that such a transform exists for general separated, self-adjoint boundary conditions...