An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
The authors propose an efficient Newton-like method of fifth order for solving scalar nonlinear equations. The new method is an extension of Newton's method and its application requires four evaluations of the given function and its first derivative, at each iteration. From the efficiency index point of view, the new iterative method has this index 1.4953, better than that of Newton's method 1.4142. Numerical examples are performed and a comparison test to other known iterative methods is made. An analysis of efficiency shows that the new algorithm is more efficient and it performs better than the classical Newton method and some other methods.
scientific article; zbMATH DE number 5510834