Open AccessQuadratic Convergence Iterative Algorithms of Taylor Series for Solving Non-linear Equations
Author(s) -
Umair Khalid Qureshi,
Zubair Ahmed Kalhoro,
Rajab A. Malookani,
Sanaullah Dehraj,
Shahid Hussain Siyal,
Ehsan Ali Buriro
Publication year - 2020
Publication title -
quaid-e-awam university research journal of engineering science and technology
Language(s) - English
Resource type - Journals
eISSN - 2523-0379
pISSN - 1605-8607
DOI - 10.52584/qrj.1802.22
Subject(s) - iterated function , iterative method , mathematics , local convergence , newton's method , convergence (economics) , quadratic equation , nonlinear system , taylor series , algorithm , newton's method in optimization , series (stratigraphy) , root finding algorithm , field (mathematics) , rate of convergence , transcendental equation , numerical analysis , computer science , mathematical analysis , key (lock) , geometry , pure mathematics , paleontology , physics , computer security , quantum mechanics , economics , biology , economic growth
Solving the root of algebraic and transcendental nonlinear equation f' (x) = 0 is a classical problem which has many interesting applications in computational mathematics and various branches of science and engineering. This paper examines the quadratic convergence iterative algorithms for solving a single root nonlinear equation which depends on the Taylor’s series and backward difference method. It is shown that the proposed iterative algorithms converge quadratically. In order to justify the results and graphs of quadratic convergence iterative algorithms, C++/MATLAB and EXCELL are used. The efficiency of the proposed iterative algorithms in comparison with Newton Raphson method and Steffensen method is illustrated via examples. Newton Raphson method fails if f' (x) = 0, whereas Steffensen method fails if the initial guess is not close enough to the actual solution. Furthermore, there are several other numerical methods which contain drawbacks and possess large number of evolution; however, the developed iterated algorithms are good in these conditions. It is found out that the quadratic convergence iterative algorithms are good achievement in the field of research for computing a single root of nonlinear equations.