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Newton’s forward interpolation method for solving nonlinear algebraic equation

Nasr Al Din Ide

Abstract

As we know, the interpolation is one of the most basic and most useful numerical techniques in Mathematics. Newton’s forward interpolation method is one of most important of these methods. Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist to find roots. But in this paper, we introduce the interpolation technique for this purpose. The proposed method derived from the newton forward interpolation method and we compared the results with another existing method (Bisection Method (BM), Regula-Falsi Method (RFM), Secant Method (SM), Newton Raphson Method (NRM)) and the method proposed by J. Sanaullah (SJM). It’s observed that the proposed method has fast convergence but it has same order of convergence of the method (SJM). Maple software is used to solve problems by different methods.


Keywords

Newton’s forward interpolation; nonlinear algebraic equations; interpolation

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References

1. Trifunov Z, Zenku L, Jusufi-Zenku T. Application of Newton’s backward interpolation using wolfram Mathematica. International Journal of Mathematics Trends and Technology 2021; 67(2): 53–56. doi: 10.14445/22315373/IJMTT-V67I2P508

2. Burden RL, Faires JD. Numerical Analysis, 9th ed. Cengage Learning; 2011.

3. Liu X, Wang X. A Family of methods for solving nonlinear equations with twelfth-order convergence. Applied Mathematics 2013; 4(2): 326–329. doi: 10.4236/am.2013.42049

4. Jamali S, Kalhoro ZA, Wasim A, et al. A new second order derivative free method for numerical solution of non-linear algebraic and transcendental equations using interpolation technique. Journal of Mechanics of Continua and Mathematical Sciences 2021; 16(4): 75–84. doi: 10.26782/jmcms.2021.04.00006

5. Mehtre VV, Sharma S. Root finding methods: Newton Raphson method. International Journal for Research in Applied Science and Engineering Technology 2019; 7(XI): 411–414. doi: 10.22214/ijraset.2019.11065

6. Ozbzn AY. Some new variants of Newton’s method. Applied Mathematics Letters 2004; 17(6): 677–682. doi: 10.1016/S0893-9659(04)90104-8

7. Omran HH. Modified third order iterative method for solving nonlinear equations. Journal of Al-Nahrain University 2013; 16(3): 239–245. doi: 10.22401/JNUS.16.3.33

8. Qureshi UK, Shaikh AA, Solangi MA. Modified free derivative open method for solving non-linear equations. Sindh University Research Journal (Science Series) 2017; 49(4): 821–824. doi: 10.26692/sujo/2017.12.0065

9. Qureshi UK, Ansari MY, Syed MR. Super linear iterated method for solving non-linear equations. Sindh University Research Journal (Science Series) 2018; 50(1).

10. Qureshi UK, Bhatti AA, Kalhoro ZA, Ali Z. On the development of numerical iterated method of Newton Raphson method for estimating nonlinear equations. University of Sindh Journal of Information and Communication Technology 2019; 3(2): 94–97.

11. Qureshi UK, Jamali S, Kalhoro ZA, Shaikh AG. Modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations. Journal of Mechanics of Continua and Mathematical Sciences 2021; 16(2): 87–101. doi: 10.26782/jmcms.2021.02.00008

12. Qureshi UK, Kalhoro ZA, Shaikh AA, Jamali S. Sixth order numerical iterated method of open methods for solving nonlinear applications problems. Proceedings of the Pakistan Academy of Sciences: A Physical and Computational Sciences 2020; 57(2): 35–40.

13. Qureshi UK, Solanki N, Ansari MY. Algorithm of difference operator for computing a single root of nonlinear equations. Punjab University Journal of Mathematics 2019; 51(4): 51–56.

14. Sangah AA, Shaikh AA, Shah SF. Comparative study of existing bracketing methods with modified bracketing algorithm for solving nonlinear equations in single variable. Sindh University Research Journal (Science Series) 2016; 48(1): 171–174.

15. Shah FA, Noor MA, Batool M. Derivative-free iterative methods for solving nonlinear equations. Applied Mathematics and Information Sciences 2014; 8(5): 2189–2193. doi: 10.12785/amis/080512

16. Subash R, Sathya S. Numerical solution of fuzzy modified Newton-Raphson method for solving non-linear equations. International Journal of Current Research 2011; 3(11): 390–392.

17. Ide NAD. On modified Newton methods for solving a non linear algebraic equations. Applied Mathematics and Computation 2008; 198(1): 138–142. doi: 10.1016/j.amc.2007.08.084

18. Ide NAD. A new hybrid iteration method for solving algebraic equations. Applied Mathematics and Computation 2008; 195(2): 772–774. doi: 10.1016/j.amc.2007.05.022

19. Ide NAD. A nonstationary Halley’s iteration method by using divided differences formula. Applied Mathematics 2012; 3(2): 169–171. doi: 10.4236/am.2012.32026

20. Ide NAD. Some new type iterative methods for solving nonlinear algebraic equation. World Applied Sciences Journal 2013; 26(10): 1330–1334. doi: 10.5829/idosi.wasj.2013.26.10.512

21. Ide NAD. Application of iterative method to nonlinear equations using homotopy perturbation methods. Journal of Basic and Applied Research International 2015; 5(3): 2395–3446.

22. Ide NAD. Some new iterative algorithms by using homotopy perturbation method for solving nonlinear algebraic equation. Asian Journal of Mathematics and Computer Research 2015; 5(3): 2395–4213.

23. Ide NAD. A new algorithm for solving nonlinear equations by using least square method. Mathematics and Computer Science 2016; 1(3): 44–47. doi: 10.11648/j.mcs.20160103.12

24. Ide NAD. Using Lagrange interpolation for solving nonlinear algebraic equations. International Journal of Theoretical and Applied Mathematics 2016; 2(2): 165–169. doi: 10.11648/j.ijtam.20160202.31

25. Ide NAD. Improvement of new eight and sixteenth order iterative methods for solving nonlinear algebraic equations by using least square method. International Journal of Scientific and Innovative Mathematical Research (IJSIMR) 2018; 6(10): 23–27. doi: 10.20431/2347-3142.0610004

26. Ide NAD. Bisection method by using fuzzy concept. International Journal of Scientific and Innovative Mathematical Research (IJSIMR) 2019; 7(4): 8–11. doi: 10.20431/2347-3142.0704002

27. Ide NAD, Aziz SNA. Using the least squares method with five points to solve algebraic equations nonlinear. International Journal of Scientific and Innovative Mathematical Research 2019; 7(5): 26–30. doi: 10.20431/2347-3142.0705005

28. Ide NAD. A new Aitken type method by using geometric mean concept. World Applied Sciences Journal 2019; 37(4): 289–292. doi: 10.5829/idosi.wasj.2019.289.292

29. Ide NAD. New modification methods for solving nonlinear algebraic equations by using Lagrange interpolation approach. Studied in Nonlinear Sciences 2019; 4(2): 23–25. doi: 10.5829/idosi.sns.2019.23.25

30. Ide NAD. Iterative method by using Tchybcheve integral for solving nonlinear algebraic equations. World Applied Sciences Journal 2019; 37(8): 661–663. doi: 10.5829/idosi.wasj.2019.661.663

31. Ide NAD. Comparison of a new modified Mcdougall-Wotherspoon method with “modified Cauchy methods using Padé approximation” to solve nonlinear equations. World Applied Sciences Journal 2020; 38(2): 106–113. doi: 10.5829/idosi.wasj.2020


DOI: https://doi.org/10.59400/jam.v1i2.64
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