PERFORMANCE EVALUATION OF NEWTON–KONTOROVICH AND ADAPTIVE NEWTON LINE SEARCH ON MULTIVARIATE NONLINEAR SYSTEMS - Syaharuddin; Ikhwanul Muslimin; Vera Mandailina; Saba Mehmood; Wasim Raza (JITK (Jurnal Ilmu Pengetahuan dan Teknologi Komputer), 2025)
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.