New predictor-corrector methods for solving nonlinear equations

作者：Wang Kun; Feng Xinlong^*

来源：Journal of Applied Mathematics and Computing, 2010, 34(1-2): 299-315.

DOI：10.1007/s12190-009-0322-x

• Initial values
• Iterative formulas
• Iterative sequences
• Newton methods
• Numerical experiments
• Predictor-corrector methods
• Regula-falsi method
• Second orders
• Steffensen method
• Two step method

In this paper, we present a new one-step iterative method for solving nonlinear equations, which inherits the advantages of both Newton's and Steffensen's methods. Moreover, two two-step methods of second-order are proposed by combining it with the regula falsi method. These new two-step methods present attractive features such as being independent of the initial values in the iterative interval, or being adaptive for the iterative formulas. The convergence of the iterative sequences is deduced. Finally, numerical experiments verify their merits.

• 出版日期2010