Increasing in three units the order of convergence of iterative methods for solving nonlinear systems

Abstract

This manuscript presents an innovative technique for high-precision iterative methods in nonlinear systems. The goal is to enhance the convergence order by three units with just one additional functional evaluation per iteration, while keeping the computational cost low. This new approach is incorporated into existing methods of order p, allowing for more accurate and efficient results. Numerical tests support the theoretical validity of the technique, highlighting its superiority over conventional p-order methods and its potential for solving complex problems. In summary, the manuscript introduces a promising technique that combines high precision and efficiency in approximating solutions for nonlinear systems, increasing the convergence order of iterative methods from p to p+3.