Abstract:
Weerakoon-Fernando Method (WFM) is a widely accepted third order iterative
method introduced in the late 90s to solve nonlinear equations. Even though it has become
so popular among numerical analysts resulting in hundreds of similar work for single variable
case, after nearly two decades, nobody took the challenge of extending the method to
multivariable systems. In this paper, we extend the WFM to functions of several variables
and provide a rigorous proof for the third order convergence. This theory was supported by
computational results using several systems of nonlinear equations. Computational algorithms
were implemented using MATLAB. We further analyze the method mathematically
and demonstrate the reason for the strong performance of WFM computationally, despite it
requiring more function evaluations
