A New Secant Type Method with Quadratic-Order Convergence

Abstract

Using the development of the second approximation, a variation of the standard secant technique for nonlinear problems has been developed. The iterative formula is created using Taylor series expansion, which includes an estimate of the second derivative of Θ(µ). It is demonstrated that the new approaches have quadratic convergence. In comparison with the Newton technique employing seven test functions in the practical application, it turns out that the performance of the method is efficient.