In this paper, we present a third-order Newton-type method to solve systems of nonlinear equations. In the first we present theoretical preliminaries of the method. Secondly, we solve some systems of nonlinear equations. All test problems show the third-order convergence of our method.
In this paper, we obtain a fourth-order convergence method to solve systems of nonlinear equations. This method is based on a quadrature formulae. A general error analysis providing the fourth order of convergence is given. Numerical examples show the fourth-order convergence. This method does not use the second-order Fréchet derivative.
Darvishi and Barati [M.T. Darvishi, A. Barati, Super cubic iterative methods to solve systems of nonlinear equations, derived a Super cubic method from the Adomian decomposition method to solve systems of nonlinear equations. The authors showed that the method is third-order convergent using classical Taylor expansion but the numerical experiments conducted… (More)
We develop a numerical algorithm for solving singularly perturbed one-dimensional parabolic convection-diffusion problems. The method comprises a standard finite difference to discretize in temporal direction and Sinc-Galerkin method in spatial direction. The convergence analysis and stability of proposed method are discussed in details, it is justifying… (More)