New Three Step Iterative Method for Solving Nonlinear Equations Using Newton-Halley Method



nonlinear equation, iterative method, Taylor expansion, Newton’s method, Halley’s method


In this paper, we present a new three step iterative method for solving solutions of the nonlinear equations in the form of . The new method is developed based on the 2nd order of Taylor series expansion with predictor-corrector technique and compared with the well-known existing methods. The comparison criterions number of iteration, reduction of the relative error graph and computational local order of convergence (CLOC). The propose method gives better results.


Malkamah, S., “Hubungan antara Volume, Kecepatan, Komposisi Kendaraan dan Tingkat Kebisingan di Jalan Rayaâ€, MSTT-UGM, Yogyakarta-Indonesia, 1992.

Djalante, S., “Analisis Tingkat Kebisingan Di Jalan Raya Yang Menggunakan Alat Pemberi Isyarat Lalu Lintas (APIL) (Studi Kasus: Simpang Ade Swalayan)â€, Jurnal SMARTek, vol. 8, no. 4, pp. 280-300, 2010.

Leslie, L.D., “Akustik Lingkungan“, Erlanga, Jakarta-Indonesia, 1985.

Smith, A.P. & Broadbent, D.E., “Non-Auditory Effects of Noise at Work A Review of the Literatureâ€, HSE Contract Research Report No, 30, HMSO, London, 1992.

Ising, H., Kruppa, B., “Health effects caused by noise: Evidence in the literature from the past 25 yearsâ€, Noise Health, vol. 6, no. 22, pp. 5-13, 2004.

Kim, K.S., Park, S.J., & Kweon, Y.J., “Highway traffic noise effects on land price in an urban areaâ€, Transportation Research Part D: Transport and Environment, vol. 12, no. 4, pp. 275-280, 2007.

Ragettli, M. S., Goudreau, S., Plante, C., Perron, S., Fournier, M., & Smargiassi, A., “Annoyance from Road Traffic, Trains, Airplanes and from Total Environmental Noise Levelsâ€, International Journal of Environmental Research and Public Health, 13(1), pp. 90, 2016.

Birk, M., Ivina O., von Klot S., Babisch W., & Heinrich J., “Road Traffic Noise: Self-Reported Noise Annoyance Versus GIS Modelled Road Traffic Noise Exposureâ€, J Enviro Monit, vol. 13, no. 11, pp. 3237-3245, 2011.

Saad, A.Q. & Arwa, A., “Effect Of Distance From Road Intersection On Developed Traffic Noise Levelsâ€, Canadian Journal of Civil Engineering, vol. 31, no. 4, pp. 533-538, 2004.

Ministry of Health, the Government of Republic of Indonesia, “Minister of Health Regulation no. 718/Menkes/Per/ XI/1987 on Noise Quality Standardsâ€, Jakarta-Indonesia, 1987.

Ministry of Environment & Forests, the Government of India 2000, “The Noise Pollution (Regulation and Control) Rules 2000â€, the Gazette of India, India, 2000.

Verheijen, E., Elbers, F., & van Golde, W., “Exploring bearable noise limits and emission ceilings for the railways Part I: National and European legislation and analysis of different noise limit systemsâ€, UIC Project ‘Bearable limits and emission ceilings’, dBvision, Netherland, 2011.

Ministry of Public Works, the Government of Republic of Indonesia, “Guidance of Noise Building Technical Planningâ€, Technical Guidance No. 036 / T / BM / 1999, Directorate General of Highways, Jakarta-Indonesia, 1999.

Radam, I.F., Mulyono, A.T., & Setiadji, B.H., 2015, “Influence of Service Factors in the Model of Public Transport Mode: A Banjarmasin – Banjarbaru Route Case Studyâ€, International Journal for Traffic and Transport Engineering, vol. 5, no. 2, pp. 108 – 119, 2015.




How to Cite

Neamvonk, A. (2018). New Three Step Iterative Method for Solving Nonlinear Equations Using Newton-Halley Method. Asian Journal of Applied Sciences, 6(2). Retrieved from