Family of fourth-order optimal classes for solving multiple-root nonlinear equations

Abstract We present a new iterative procedure for solving nonlinear equations with multiple roots high efficiency. Starting from the arithmetic mean of Newton’s and Chebysev’s methods, we generate two-step scheme using weight functions, resulting in family methods that satisfies Kung Traub conjecture, yielding an optimal different choices function. have performed in-depth analysis stability members, order to select those members highest application mathematical chemistry problems. show good characteristics selected by applying them on four relevant chemical