METODE ITERASI BERTIPE NEWTON UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR DENGAN ORDE KONVERGENSI SEBARANG BILANGAN BULAT

Abstract

This article discusses an analytic study of combining iterative methods of order p and q with p and q integers to Newton’s method to obtain a Newton-type iteration method of order p + q. This new method can also be applied to solve systems of nonlinear equations. Numerical computations are carried out consecutively for a method of second and third order, which produce a Newton-type method of fifth order, and methods of third and fifth order, which produce a Newton-type method  of eighth order. The test results support the analytical studies.