Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 5 3 2024 07 01 Interpolatory four-parametric adaptive method with memory for solving nonlinear equations 275 287 5248 10.22060/ajmc.2023.22090.1132 EN Vali Torkashvand Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran Journal Article 2023 01 10 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. https://ajmc.aut.ac.ir/article_5248_81bc798a42a7ce40810bf523f24deee1.pdf