Interpolatory four-parametric adaptive method with memory for solving nonlinear equations

The adaptive technique enables us to achieve the highest efficiency index theoretically and practically. The idea of introducing an adaptive self-accelerator (via all the old information for Steffensen-type methods) is new and efficient to obtain the highest efficiency index. In this work, we have used four self-accelerating parameters and have increased the order of convergence from 8 to 16, i. e. any new function evaluations improve the convergence order up to 100%. The numerical results are compared without and with memory methods. It confirms that the proposed methods have more efficiency index.