Enhanced Ninth-Order Memory-Based Iterative Technique for Efficiently Solving Nonlinear Equations - Shubham Kumar Mittal; Sunil Panday; Lorentz Jäntschi (Mathematics)
In this article, we present a novel three-step with-memory iterative method for solving nonlinear equations. We have improved the convergence order of a well-known optimal eighth-order iterative method by converting it into a with-memory version. The Hermite interpolating polynomial is utilized to compute a self-accelerating parameter that improves the convergence order. The proposed uni-parametric with-memory iterative method improves its R-order of convergence from 8 to <semantics>8.8989</semantics>. Additionally, no more function evaluations are required to achieve this improvement in convergence order. Furthermore, the efficiency index has increased from <semantics>1.6818</semantics> to <semantics>1.7272</semantics>. The proposed method is shown to be more effective than some well-known existing methods, as shown by extensive numerical testing on a variety of problems.