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All Journal Jurnal Sains dan Teknologi AKSIOMA: Jurnal Program Studi Pendidikan Matematika Jurnal Elemen Jurnal ELTIKOM : Jurnal Teknik Elektro, Teknologi Informasi dan Komputer JITK (Jurnal Ilmu Pengetahuan dan Komputer) Jurnal Ulul Albab JTAM (Jurnal Teori dan Aplikasi Matematika) Mosharafa: Jurnal Pendidikan Matematika Advance Sustainable Science, Engineering and Technology (ASSET)
Mehmood, Saba
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Aerospace Engineering Humanities Chemistry Computer Science & IT Control & Systems Engineering Education Electrical & Electronics Engineering Engineering Industrial & Manufacturing Engineering Mathematics Social Sciences Other

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Accuracy Comparison of Multivariate Newton-Raphson and Newton-Kantorovich Methods through Numerical Simulation in Nonlinear Systems Syaharuddin; Hidayah, Hendi; Mahsup, Mahsup; Mehmood, Saba; Raza, Wasim
Jurnal ELTIKOM : Jurnal Teknik Elektro, Teknologi Informasi dan Komputer Vol. 10 No. 1 (2026)
Publisher : P3M Politeknik Negeri Banjarmasin

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31961/eltikom.v10i1.1971

Abstract

Nonlinear systems of equations often appear in various fields of science and generally cannot be solved analytically, so numerical methods are required. However, previous studies have not provided a direct comparison of the accuracy and efficiency of the Multivariate Newton-Raphson method and the Newton-Kantorovich method when applied to the same nonlinear system, creating a gap in understanding their relative performance. This study aims to analyze and compare the performance of two numerical methods, namely the Newton-Raphson method and the Newton-Kantorovich method, in solving nonlinear systems of equations numerically. The evaluation is based on the convergence rate, result accuracy, and iteration efficiency of each method. The nonlinear system used involves trigonometric, exponential, and polynomial functions. Simulations were conducted twice using three equations directly for each method. The error tolerance was set at 0.001, with a maximum of 100 iterations. The simulation results showed that the Multivariate Newton-Raphson method had the best performance, requiring only 7 iterations to achieve convergence with a very small error of 2.711×10^(-7). In contrast, the Newton-Kantorovich method required 21 iterations and produced an error of 6.770×10^(-5), indicating slower convergence and lower efficiency. Based on these results, it can be concluded that the Multivariate Newton-Raphson method is the more accurate and efficient method for solving nonlinear systems of equations through numerical simulation. This finding contributes to the selection of an appropriate numerical method and opens opportunities for further exploration in higher-dimensional systems.
Co-Authors Abdillah Abdillah Abdillah Adzikya, Dieky Aftab Ahmad, Aftab Asmaul Husnah Balasubramanian, Deepa Chidambaram, Natarajan Dieky Adzkiya Fitriatunnisa, Ririn Hameed, Shahzaib Hidayah, Hendi Hussain, Muhammad Jafar Intan Dwi Hastuti Iqbal, Zainab Kamran, Muhammad Khan, Aamir Hussain Mahsup Mahsup, Mahsup Mariyati, Yuni Meyundasari, Maulidia Dwi Muslimin, Ikhwanul Nadila, Desi Raza, Sajid Raza, Wasim Subchan, Subchan Syaharuddin Syaharuddin Syaharuddin Syaharudin, Syaharudin Usman, Muhammad Talha Vera Mandailina Vera Mandailina, Vera Wasti, Syeda Rabbia