OICC Press Mathematical Analysis and its Contemporary Applications 4 3 2022 04 01 Extension of the double Newton's method convergence order via the bi-variate power series weight function for solving nonlinear models 10.30495/maca.2022.1954323.1052 EN Oghovese Ogbereyivwe Delta State University of Science and Technology, Ozoro, Nigeria Simon Ajiroghene Ogumeyo Delta State University of Science and Technology, Ozoro, Nigeria Journal Article 2022 04 01 This manuscript put forward one and two-parameter families of modified double Newton iterative structure with convergence order six, for approximation of the solution of nonlinear model. The modification technique involves the introduction of quotient of two converging bi-variate power series based weight function to the second step of the double Newton's method. Some particular members of the developed methods have experimented on some physical phenomena modeled into nonlinear equations and results compared with some existing methods.