In this work we propose an improvement to the popular Newton’s method based on the contra-harmonic mean while using quadrature rule derived from a Ostrowski-Gräuss type inequality developed in [19]. The order of convergence of this method for solving non-linear equations which have simple roots is shown to be three. Computer Algebra Systems (CAS), such as MAPLE 18 package, can be used successfu...

Efficiency is generally the most important aspect to take into account when choosing an iterative method to approximate a solution of an equation, but is not the only aspect to consider in the iterative process. Another important aspect to consider is the accessibility of the iterative process, which shows the domain of starting points from which the iterative process converges to a solution of...

S.K. Khattri Department of Engineering Stord Haugesund University College Norway Email: [email protected] Abstract. We present a local convergence analysis of a family of third order methods for approximating a locally unique solution of nonlinear equations in a Banach space setting. Recently, the semilocal convergence analysis of this method was studied by Chun, Stănică and Neta in [10]. T...

In this paper we present a new one-parameter family of iterative methods to solve nonlinear equations which includes some well-known third-order methods as particular ones. The convergence analysis shows that the order of convergence of each method of the family is three. Numerical examples are given to illustrate the efficiency and performance of the presented methods. 2006 Elsevier Inc. All r...

In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial compu...

A new family of binomial trees as approximations to the Black–Scholes model is introduced. For this class of trees, the existence of complete asymptotic expansions for the prices of vanilla European options is demonstrated and the first three terms are explicitly computed. As special cases, a tree with third order convergence is constructed and the conjecture of Leisen and Reimer that their tre...