Optimal fourth-order iterative methods free from derivatives. (English) Zbl 1265.65101

Soleymani, F.

Miskolc Math. Notes 12, No. 2, 255-264 (2011).

Summary: The construction of optimal fourth-order iterative schemes for solving univariate nonlinear equations is discussed. Per iteration, the methods consist of three evaluations of the function and they are free from any derivative calculation which property is so fruitful in engineering problems. We analytically show the fourth-order convergence. Numerical examples are considered to confirm the applicability and to justify the rapid convergence of the novel iterative algorithms.

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

optimal root solver; simple zero; derivative-free methods; nonlinear equations; order of convergence; Steffensen’s method; fourth-order iterative schemes; numerical examples