Computer Oriented Numerical Scheme for Solving Engineering Problems

In this study, we construct a family of single root finding method optimal order four and then generalize for estimating all roots non-linear equation simultaneously. Convergence analysis proves that the local convergence is in case iterative six simultaneous determination equation. Some equations are taken from physics, chemistry engineering to present performance efficiency newly constructed method. real world applications fluid mechanics, i.e., permeability biogels biomedical which includes blood Rheology-Model as an intermediate result give some nonlinear equations. These solved using developed schemes. Newly schemes reach exact values on initial guessed within given tolerance, very less number function evaluations each step. Local computed CAS-Maple. computational convergence, CPU-time, absolute residuals errors calculated elaborate efficiency, robustness authentication its domain.