Research Article

A new variant of midpoint Newton’s method for solving nonlinear models

Abstract: Numerous real-world models in engineering and applied sciences frequently involve nonlinear equations that call for trustworthy numerical techniques to solve. Existing iterative methods are constantly being modified, and new ones are being introduced as computational science research expands quickly. Nevertheless, these numerical methods may have high computational cost, but they do have a faster rate of convergence. In this paper, our aim is develop a new variant of midpoint third order iterative methods for solving nonlinear equation. The main theorem proves the third-order convergence, which uses just three function evaluations with 2f and 1f′. We apply the proposed methods to a number of nonlinear models in the medical sciences, such as the law of blood flow, blood rheology, fluid permeability in biogels, and the human body’s temperature control, in order to verify the theoretical results and show its effectiveness. The number of iterations, error in subsequent approximations, computational convergence order (CCO), and CPU time (seconds) are used to assess the method’s performance.