Mudassir Shams¹, Nasreen Kausar^2,*, Shams Forruque Ahmed³, Irfan Anjum Badruddin⁴, Syed Javed⁴

CMC-Computers, Materials & Continua, Vol.74, No.3, pp. 5331-5347, 2023, DOI:10.32604/cmc.2023.033528

Abstract A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this paper. Convergence analysis demonstrates that the local order of convergence of the numerical method is five. The computer algebra system CAS-Maple, Mathematica, or MATLAB was the primary tool for dealing with difficult problems since it allows for the handling and manipulation of complex mathematical equations and other mathematical objects. Several numerical examples are provided to demonstrate the properties of the proposed rapidly convergent algorithms. A dynamic evaluation of the presented methods is also presented utilizing basins… More >

Mudassir Shams¹, Naila Rafiq², Nasreen Kausar³, Nazir Ahmad Mir², Ahmad Alalyani^4,*

Computer Systems Science and Engineering, Vol.42, No.2, pp. 689-701, 2022, DOI: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… More >