Nonlinear equations are used to describe and comprehend a wide range of complicated processes seen in both natural and manmade systems, as well as biomedical engineering. Their research has resulted in substantial theoretical and practical advances, cementing their place as a foundation for modern science and biomedical engineering. Since it is extremely complex and challenging to solve these nonlinear problems using analytical methods, we turn to numerical schemes. In this chapter, we present a novel single-step optimal family and then apply it as a correction fundamental parallel iterative approach to increase the convergence rate from two to three. Using basin attraction to determine the optimal parameter values in a single-step technique and then applying these values to a newly developed parallel scheme to enhance accuracy when compared to existing methods. The numerical findings of the biomedical engineering application, which involves the equilibrium binding of multivalent ligands to cell surfaces in solution and osteoporosis in Chinese women, reveal that our methods outperform existing methods in terms of error and computing time.