An Orthogonal Polynomial Based Iterative Procedure for Finding the Root of the Equation f (x) = 0

Iterative methods provide hope for many nonlinear engineering problems that cannot be solved through analytic procedures. In this article, orthogonal polynomial based iterative schemes are developed for the approximate solutions of nonlinear algebraic and transcendental equations. Basically, Mamadu-Njoseh orthogonal polynomials are employed as basis functions to derive the new iterative schemes called the “Mamadu \(\Delta\) 2 and \(\Delta\) 3 iterative schemes”. Convergence analysis of the schemes shows the convergence rate as of order 3 and 4, respectively. Numerical experimental of the new schemes show the feasibility and correctness of the method.