He's iteration formulation for solving nonlinear algebraic equations

A More Effective Iteration Method for Solving Algebraic Equations

This note is concerned with the iteration numerical scheme for solving nonlinear algebraic equations. A more effective and more rapidly convergent iteration method is proposed, which improves the convergence of the previous numerical schemes and also eliminates the need of careful initial points selection in the previous work given by J.-H. He [Appl. Math. Comp. 135 (2003) 81-84].

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

THE USE OF THE HE'S ITERATION METHOD FOR SOLVING NONLINEAR EQUATIONS USING CADNA LIBRARY

In this paper, we apply the Newton’s and He’s iteration formulas in order to solve the nonlinear algebraic equations. In this case, we use the stochastic arithmetic and the CESTAC method to validate the results. We show that the He’s iteration formula is more reliable than the Newton’s iteration formula by using the CADNA library.

Variational Iteration Method for Solving Nonlinear WBK Equations

In this letter, He’s Variational iteration method (VIM) is implemented for solving the nonlinear Whitham-Broer-Kaup partial differential equations. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The results are compared with those obtained by t...

ABS methods for nonlinear systems of algebraic equations

 Abstract    This paper gives a survey of the theory and practice of nonlinear ABS methods including various types of generalizations and computer testing. We also show three applications to special problems, two of which are new.