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# Computer Oriented Numerical Scheme for Solving Engineering Problems

1 Department of Mathematica and Statistics, Riphah International University, I-14, Islamabad 44000, Pakistan
2 Department of Mathematics, NUML, Islamabad 44000, Pakistan
3 Department of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler, 34210, Istanbul, Turkey
4 Department of Mathematics, Faculty of Science and Arts in ALmandaq, Al-Baha University, Al-Baha, Saudi Arabia

* Corresponding Author: Ahmad Alalyani. Email:

Computer Systems Science and Engineering 2022, 42(2), 689-701. https://doi.org/10.32604/csse.2022.022269

## Abstract

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

## Keywords

APA Style
Shams, M., Rafiq, N., Kausar, N., Mir, N.A., Alalyani, A. (2022). Computer oriented numerical scheme for solving engineering problems. Computer Systems Science and Engineering, 42(2), 689-701. https://doi.org/10.32604/csse.2022.022269
Vancouver Style
Shams M, Rafiq N, Kausar N, Mir NA, Alalyani A. Computer oriented numerical scheme for solving engineering problems. Comput Syst Sci Eng. 2022;42(2):689-701 https://doi.org/10.32604/csse.2022.022269
IEEE Style
M. Shams, N. Rafiq, N. Kausar, N.A. Mir, and A. Alalyani "Computer Oriented Numerical Scheme for Solving Engineering Problems," Comput. Syst. Sci. Eng., vol. 42, no. 2, pp. 689-701. 2022. https://doi.org/10.32604/csse.2022.022269

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