Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

AN ITERATIVE METHOD WITH SIX-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

An Operator Splitting Method for Nonlinear Convection-diffusion Equations

We present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection di usion equation ut r f u u The method is based on the use of operator splitting to isolate the convection part and the di usion part of the equation In the casem dimensional splitting is used to reduce the m dimensional convection problem to a series of one di...

An Efficient Optimal Eighth-order Iterative Method for Solving Nonlinear Equations

In this paper we established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative). Convergence analysis shows that this method is eighth-order convergent which is also substantiated through the numerical works. Computational resul...

An Iterative Method with Fifth-Order Convergence for Nonlinear Equations

In this paper, we suggest and analyze a new four-step iterative method for solving nonlinear equations involving only first derivative of the function using a new decomposition technique which is due to Noor [11] and Noor and Noor [16]. We show that this new iterative method has fifth-order of convergence. Several numerical examples are given to illustrate the efficiency and performance of the ...