NILAI AWAL PADA METODE NEWTON-RAPHSON YANG DIMODIFIKASI DALAM PENENTUAN AKAR PERSAMAAN
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Metode Newton-Raphson, Metode Newton-Raphson Modifikasi, akar persamaan, akar ganda
Abstract
Penentuan akar suatu persamaan berarti membuat persamaan tersebut sama dengan nol f(x)=0. Beberapa metode numerik bisa digunakan untuk menentukan akar persamaan yang bentuknya sangat kompleks. Akan tetapi untuk akar ganda, beberapa metode numerik seperti metode bisection, metode regulafalsi, metode Newton-Raphson, metode Secant memiliki kesulitan. Penelitian ini bertujuan untuk mengetahui pengaruh penentuan nilai awal pada metode Newton-Raphson yang dimodifikasi dalam mementukan akar persamaan yang memiliki akar ganda. Simulasi dilakukan pada persamaan yang memiliki 1 akar tunggal dan 2 akar ganda atau lebih. Dengan metode Newton-Raphson nilai awal yang dipilih dekat dengan akar tunggal maka akarnya terletak pada sekitar atau sama dengan akar tunggal. Namun dengan metode Newton-Raphson yang dimodifikasi pemilihan nilai awal lebih dekat dengan akar tunggal, nilai akar yang dihasilkan menunjuk pada akar ganda.
References
Dey, A., 2015, Mathematical Model Formulation and Comparison Study of Various Methods of Root-Finding Problems, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 2 Ver. III (Mar - Apr. 2015), PP 64-71.
Imran, M., Syamsudhuha,. Putra, S., 2016, A NEW FAMILY OF SECANT-LIKE METHOD WITH SUPER-LINEAR CONVERGENCE, International Journal of Pure and Applied Mathematics Volume 110 No. 1 2016, 1-7 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v110i1.1.
Magrean, A.A., Argyros, I.K., 2015, EXPANDING THE APPLICABILITY OF SECANT METHOD WITH APPLICATIONS, ull. Korean Math. Soc. 52 (2015), No. 3, pp. 865–880 http://dx.doi.org/10.4134/BKMS.2015.52.3.865.
Hussein, K.A., Altaee, A.A.H., Hoomod, H.K., 2015, Parallel Hybrid Algorithm of Bisection and Newton-RaphsoMethods to Find Non-Linear Equations Roots, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319765X Volume 11, Issue 4 Ver. II (Jul - Aug. 2015), PP 32-36.
Ehiwario, J.C., Aghamie, S.O., 2014, Comparative Study of Bisection, Newton-Raphson and Secant Methods of Root- Finding Problems, IOSR Journal of Engineering (IOSRJEN) ISSN (e): 2250-3021, ISSN (p): 2278-8719. Vol. 04, Issue 04 (April. 2014), ||V1|| PP 01-07.
Ahmad, A. G., 2015, Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems
, International Journal of Mathematics Trends and Technology- Volume 19 Number 2 Mar 2015.
Kumar, R., Vipan, 2015, Comparative Analysis of Convergence of Various Numerical Methods, Journal of Computer and Mathematical Sciences, Vol.6(6),290-297, June 2015 ISSN 0976-5727 (Print), ISSN 2319-8133 (Online),(An International Research Journal), www.compmathjournal.org.
Sharma,S.K., 2017, A Comparative Analysis of Rate of Convergence For Linear And Quadratic Approximations in N-R Method , World Journal of Research and Review (WJRR) ISSN:2455-3956, Volume-4, Issue-5, May 2017 Pages 94-96.
Mohammad, H., 2015, A Simple Hybrid Method for Finding the Root of Nonlinear Equations IJSRST | Volume 1 | Issue 4 | Print ISSN: 2395-6011 | Online ISSN: 2395602X IJSRST151420 | Received: 09 October 2015 | Accepted: 16 October 2015 | September-October 2015 [(1)4: 80-83].
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