Comparative Study of Bisection, Newton, Horner’s Method for Solving Nonlinear Equation
Abstract
The Bisection, Newton and Horner’s method are used to compare the efficiency to solve nonlinear function such as trigonometric, exponential, logarithmic and cubic polynomial function. Although these methods are considered as alternative, the methods also possess error compared to the exact value. The efficiency is measured by the error produced at the fixed iteration. The methods are converted into C language and executed by using maple 18.
##Keywords:##
Bisection method, Newton method, Horner’s method.
Published
Jul 30, 2021
How to Cite
AZIZ, Amiruddin Ab et al.
Comparative Study of Bisection, Newton, Horner’s Method for Solving Nonlinear Equation.
Journal of Ocean, Mechanical and Aerospace -science and engineering-, [S.l.], v. 65, n. 2, p. 36-39, july 2021.
ISSN 2527-6085.
Available at: <https://isomase.org/Journals/index.php/jomase/article/view/238>. Date accessed: 03 june 2026.
doi: http://dx.doi.org/10.36842/jomase.v65i2.238.
References
[1] Boyd, S., Balakrishnan, V., & Kabamba, P. (1989). A bisection method for computing the H norm of a transfer matrix and related problems. Mathematics of Control, Signals and Systems, 2(3), 207-219.
[2] Artashkin, E.P. (2016). BISECTION METHOD. APRIORI. CЕРИЯ: ЕСТЕСТВЕÐÐЫЕ И ТЕХÐИЧЕСКИЕ ÐÐУКИ, (6), 4.
[3] Iwetan, C.N., Fuwape, I. A., Olajide, M.S., & Adenodi, R.A. (2012). Comparative Study of the Bisection and Newton Methods in solving for Zero and Extremes of a Single-Variable Function. J. of NAMP, 21, 173–176.
[4] Charles, J. (2008). Comparative Study of Bisection, Newton-Raphson and Secant. Comparative Study of Bisection, Newton-Raphson and Secant - Root Finding Method.
[5] Matveev, M.N. (2016). An intermediate value theorem for face polytopes. Lobachevskii Journal of Mathematics, 37(3), 307–315. https://doi.org/10.1134/S1995080216030173.
[6] Namekar, S. (2019). Role of Bisection Method. International Journal for Research in Applied Science and Engineering Technology, 7(11), 426–429. https://doi.org/10.22214/ijraset.2019.11068.
[7] Zaslavski, A. J. (2016). Newton’s method. In Springer Optimization and Its Applications (Vol. 108, pp. 265–296). https://doi.org/10.1007/978-3-319-30921-7_16.
[8] He, T.-X., & Shiue, P. J.-S. (2012). A note on Horner’s method. J. Concr. Appl. Math., 10(1-2), 53-64.
[9] Muller, J.-M., & Muller, J.-M. (2016). Polynomial Evaluation. In Elementary Functions (pp. 81–100). https://doi.org/10.1007/978-1-4899-7983-4_5.
[10] Burden, A., L. Burden, R., & Douglas Faires, J. (2016). Numerical Analysis, 10th ed. Communications of the ACM (Vol. 10). https://doi.org/10.13140/2.1.4830.2406.
[2] Artashkin, E.P. (2016). BISECTION METHOD. APRIORI. CЕРИЯ: ЕСТЕСТВЕÐÐЫЕ И ТЕХÐИЧЕСКИЕ ÐÐУКИ, (6), 4.
[3] Iwetan, C.N., Fuwape, I. A., Olajide, M.S., & Adenodi, R.A. (2012). Comparative Study of the Bisection and Newton Methods in solving for Zero and Extremes of a Single-Variable Function. J. of NAMP, 21, 173–176.
[4] Charles, J. (2008). Comparative Study of Bisection, Newton-Raphson and Secant. Comparative Study of Bisection, Newton-Raphson and Secant - Root Finding Method.
[5] Matveev, M.N. (2016). An intermediate value theorem for face polytopes. Lobachevskii Journal of Mathematics, 37(3), 307–315. https://doi.org/10.1134/S1995080216030173.
[6] Namekar, S. (2019). Role of Bisection Method. International Journal for Research in Applied Science and Engineering Technology, 7(11), 426–429. https://doi.org/10.22214/ijraset.2019.11068.
[7] Zaslavski, A. J. (2016). Newton’s method. In Springer Optimization and Its Applications (Vol. 108, pp. 265–296). https://doi.org/10.1007/978-3-319-30921-7_16.
[8] He, T.-X., & Shiue, P. J.-S. (2012). A note on Horner’s method. J. Concr. Appl. Math., 10(1-2), 53-64.
[9] Muller, J.-M., & Muller, J.-M. (2016). Polynomial Evaluation. In Elementary Functions (pp. 81–100). https://doi.org/10.1007/978-1-4899-7983-4_5.
[10] Burden, A., L. Burden, R., & Douglas Faires, J. (2016). Numerical Analysis, 10th ed. Communications of the ACM (Vol. 10). https://doi.org/10.13140/2.1.4830.2406.
