Eighteenth Order Convergent Method for Solving Non-Linear Equations

Abstract

ABSTRACT:In this paper, we suggest and discuss an iterative method for solving nonlinear equations of the type f(x) = 0 having eighteenth order convergence. This new technique based on Newton's method and extrapolated Newton's method. This method is compared with the existing ones through some numerical examples to exhibit its superiority.

Refinement of SOR Iterative Method for the Linear Rational Finite Difference Solution of Second-Order Fredholm Integro-Differential Equations

“…where the values of matrices and are determined as stated in Equation (18). Based on formulation of the RSOR method in (22), the convergence analysis of this method has been discussed by [20].…”

“…For this reason, we mainly implement iterative methods to achieve the numerical solution of a linear system. Considering that the SOR iterative method has the advantage of a flexible selection of relaxation factor values, we improved the SOR iterative method again and obtained the refined iterative methods which were discussed by [8] and [20]. In the end, we investigate the performance of the RSOR iterative method [20] together with the three-point newly established LRFD (3LRFD) formula to obtain the numerical solution of the linear system, which is generated by the corresponding three-point linear rational finite difference-quadrature approximation equations.…”