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All Journal Jurnal ELTIKOM : Jurnal Teknik Elektro, Teknologi Informasi dan Komputer JITK (Jurnal Ilmu Pengetahuan dan Komputer)
Wasim Raza
University of Sargodha
Aerospace Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Engineering

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PERFORMANCE EVALUATION OF NEWTON–KONTOROVICH AND ADAPTIVE NEWTON LINE SEARCH ON MULTIVARIATE NONLINEAR SYSTEMS Ikhwanul Muslimin; Syaharuddin; Vera Mandailina; Saba Mehmood; Wasim Raza
JITK (Jurnal Ilmu Pengetahuan dan Teknologi Komputer) Vol. 11 No. 2 (2025): JITK Issue November 2025
Publisher : LPPM Nusa Mandiri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33480/jitk.v11i2.7370

Abstract

Solving multivariate nonlinear systems is essential in engineering, physics, and applied sciences. This study compares the performance of two numerical methods—Newton–Kontorovich and Interactive Newton–Raphson with Line Search—on trigonometric and exponential nonlinear systems. The methods are evaluated based on convergence rate, accuracy, and iteration efficiency through numerical simulations using MATLAB. The Newton–Kontorovich method, typically used for integral or differential equations, is compared with the adaptive line search strategy that enhances global convergence. Results show that the Interactive Newton–Raphson method achieves a smaller final error (5.95×10⁻²) with stable convergence, while Newton–Kontorovich converges in fewer iterations but with larger error (3.126). These findings highlight the superiority of adaptive strategies for complex nonlinear systems. Practical implications include improved numerical reliability for applications in structural engineering, optimization, and scientific modeling.
Accuracy Comparison of Multivariate Newton-Raphson and Newton-Kantorovich Methods through Numerical Simulation in Nonlinear Systems Syaharuddin; Hendi Hidayah; Mahsup Mahsup; Saba Mehmood; Wasim Raza
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 Hendi Hidayah Ikhwanul Muslimin Mahsup Mahsup Saba Mehmood Saba Mehmood Syaharuddin Syaharuddin Syaharuddin Vera Mandailina