Open AccessOn numerical schemes for determination of all roots simultaneously of non-linear equation
Author(s) -
Nazir Ahmad Mir,
Mochamad Anwar,
Mudassir Shams,
Naila Rafiq,
Saima Akram
Publication year - 2022
Publication title -
mehran university research journal of engineering and technology
Language(s) - English
Resource type - Journals
eISSN - 2413-7219
pISSN - 0254-7821
DOI - 10.22581/muet1982.2202.20
Subject(s) - convergence (economics) , mathematics , residual , linear equation , variable (mathematics) , root (linguistics) , mathematical optimization , construct (python library) , numerical analysis , iterative method , computer science , algorithm , mathematical analysis , linguistics , philosophy , economics , programming language , economic growth
In this article, we first construct family of two-step optimal fourth order iterative methods for finding single root of non-linear equation. We then extend these methods for determining all the distinct as well as multiple roots of single variable non-linear equation simultaneously. Convergence analysis is presented for both the cases to show that the optimal order of convergence is 4 in case of single root finding method and 6 for simultaneous determination of all distinct as well as multiple roots of a non-linear equation. The computational cost, basins of attraction, computational efficiency, log of residual fall and numerical test functions validate that the newly constructed methods are more efficient as compared to the existing methods in the literature.