Abstract:
This article discusses a simple modification of the variants of Newton's
method for solving nonlinear equations. Jain (2013) combines the use of the
Secant method with Trapezoidal Newton's method developed by Weerakon and
Fernando (2000) and produces new combination Secant-Trapezoid Newton
method that has fourth-order convergence. Using Jain's idea, the authors combine
the use of the Secant method with two other variants of Newton's method
developed by Ozban (2004), namely Arithmetic and Harmonic Newton. It turns
out that both the new combinations are has fourth-order convergence. Numerical
calculation with several examples of nonlinear equations is used to show that both
the new combinations method are comparable with other fourth-order methods
