PERFORMANCE EVALUATION OF NEWTON–KONTOROVICH AND ADAPTIVE NEWTON LINE SEARCH ON MULTIVARIATE NONLINEAR SYSTEMS
DOI:
https://doi.org/10.33480/jitk.v11i2.7370Kata Kunci:
Interactive Newton Line Search , Newton Kontorovich , Numerical methods , Numerical SimulationAbstrak
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.
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Referensi
F. Istiqomah, “Penyelesaian Sistem Persamaan Non-Linier Dengan Metode Perbaikan Regula Falsi Menggunakan Bahasa Pemrograman Javascript,” J. Teknol. dan Bisnis, vol. 4, no. 1, pp. 17–22, 2022, doi: 10.37087/jtb.v4i1.75.
A. M. Nugraha and N. Nurullaeli, “GRAPHICAL USER INTRFACE (GUI) MATLAB UNTUK PENYELESAIAN PERSAMAAN DIFERENSIAL BIASA ORDE SATU,” Semnas Ristek (Seminar Nas. Ris. dan Inov. Teknol., vol. 7, no. 1, pp. 182–185, 2023, doi: 10.30998/semnasristek.v7i1.6269.
Parida, Melisa, M. Safitri, and N. Zakiah, “Implementasi Penerapan Fungsi Nonliner Dalam Matematika Ekonomi Pada Kehidupan Sehari-Hari,” Al-Aqlu J. Mat. Tek. dan Sains, vol. 2, no. 1, pp. 9–16, 2024, doi: 10.59896/aqlu.v2i1.39.
K. A. Sujaya, Sudi Prayitno, Nani Kurniati, and Nyoman Sridana, “Efektivitas Metode Brent dalam Penyelesaian Masalah Break Even Point Menggunakan Pemrograman Pascal,” Mandalika Math. Educ. J., vol. 6, no. 1, pp. 120–130, 2024, doi: 10.29303/jm.v6i1.6923.
R. K. Muslimov, “On a new paradigm for the development of the oil and gas complex in russia,” 2021 doi: 10.24887/0028-2448-2021-3-8-13.
A. Aghili, “Some identities for Mellin, Kontorovich-Lebedev transforms with applications,” Adv. Stud. Euro-Tbilisi Math. J., vol. 14, no. 2, pp. 239–253, 2021, doi: 10.32513/tmj/19322008136.
A. Calvo-Rivera, A. L. Velikovich, and C. Huete, “On the stability of piston-driven planar shocks,” J. Fluid Mech., vol. 964, no. 33, pp. 1–38, 2023, doi: 10.1017/jfm.2023.373.
K. Tomashchuk, “Methods for the Numerical Analysis of Boundary Value Problem of Partial Differential Equations Based on Kolmogorov Superposition Theorem,” vol. 1, no. 1, pp. 1–13, 2021, doi: https://doi.org/10.48550/arXiv.2111.00946.
J. Lee, H. J. Bong, and M. G. Lee, “Return mapping with a line search method for integrating stress of the distortional hardening law with differential softening,” Comput. Struct., vol. 257, no. december 2021, p. 106652, 2021, doi: 10.1016/j.compstruc.2021.106652.
A. G. Wills and T. B. Schön, “Stochastic quasi-Newton with line-search regularisation,” Automatica, vol. 127, no. may 2021, p. 105903, 2021, doi: 10.1016/j.automatica.2021.109503.
R. Verma and A. Rathore, “Optimal Placement of Facts Device Considering Voltage Stability and Losses using Teaching Learning based Optimization,” J. Inst. Eng. Ser. B, vol. 102, pp. 771–776, 2021, doi: 10.1007/s40031-021-00582-w.
A. Marengo and U. Perego, “A small deformations effective stress model of gradient plasticity phase-field fracture,” Comput. Methods Appl. Mech. Eng., vol. 409, no. 1, p. 115992, 2023, doi: 10.1016/j.cma.2023.115992.
J. S. KISETA and R. L. AKUMOSO, “A Review of Well-Known Robust Line Search and Trust Region Numerical Optimization Algorithms for Solving Nonlinear Least-Squares Problems,” Int. Sci. Rev., 2021, doi: 10.47285/isr.v2i3.106.
D. B. Kuryliak, “Wave diffraction from the PEC finite wedge,” J. Eng. Math., vol. 134, no. 5, 2022, doi: 10.1007/s10665-022-10222-x.
S. Regmi, I. K. Argyros, S. George, and J. Warden, “A Unified Kantorovich-type Convergence Analysis of Newton-like Methods for Solving Generalized Equations under the Aubin Property,” Eur. J. Math. Anal., vol. 4, p. 3, 2024, doi: 10.28924/ada/ma.4.3.
H. Bin Jebreen, H. Wang, and Y. Chalco-Cano, “Efficient Newton-Type Solvers Based on for Finding the Solution of Nonlinear Algebraic Problems,” Axioms, vol. 13, no. 12, p. 880, 2024, doi: 10.3390/axioms13120880.
A. F. Kirani, R. Ibnas, and I. Syata, “SOLUSI NUMERIK SISTEM PERSAMAAN NON LINEAR DALAM REAKSI STEAM REFORMING MENGGUNAKAN METODE NEWTON-RHAPSON [ Numerical Solution of Non-Linear Equation System in Steam Reforming Reaction Using Newthon-Raphson Method ],” vol. 3, no. September 2024, pp. 43–55, 2025, doi: ttps://doi.org/10.59896/aqlu.v3i1.105.
R. Abreu, C. Mejia, and D. Roehl, “A comprehensive implicit substepping integration scheme for multisurface plasticity,” Int. J. Numer. Methods Eng., vol. 123, no. 1, pp. 2–303, 2022, doi: 10.1002/nme.6826.
I. D. Kan, “A strengthening of the Bourgain-Kontorovich method: Three new theorems,” Sb. Math., vol. 212, no. 7, pp. 921–964, 2021, doi: 10.1070/SM9437.
T. Tuan, “Composition structure of polyconvolution associated with index Kontorovich-Lebedev transform and Fourier integrals,” no. February, pp. 1–16, 2025, doi: https://dx.doi.org/10.1080/10652469.2025.2536167.
T. Mánik, “A natural vector/matrix notation applied in an efficient and robust return-mapping algorithm for advanced yield functions,” Eur. J. Mech. A/Solids, vol. 90, no. 2021, p. 104357, 2021, doi: 10.1016/j.euromechsol.2021.104357.
T. Yigit and M. Millidere, “The Local Search-Based Genetic Algorithm in Aircraft Trim,” in AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021, 2021. doi: 10.2514/6.2021-2999.
Y. Mumtazi, N. Hikmah, and S. Prayitno, “Comparison of Steffensen and Secant Methods in Determining Non- Linear Function Roots Using Hypertext Preprocessor ( PHP ) Programmer,” vol. 5, no. 3, pp. 418–424, 2024, doi: https://doi.org/10.29303/goescienceed.v5i3.393.
N. Rahmatullah, “Perbandingan Metode Newton Raphson dan Metode Steffensen dalam Penentuan Akar Fungsi Non-Linier Menggunakan Pemrograman,” vol. 10, no. 2, pp. 300–312, 2025, doi: https://doi.org/10.23969/jp.v10i02.26961.
Silviana Dewi Anastasya, “Implementasi Metode Fixed-Point Dan Newton-Raphson Dalam Penyelesaian Persamaan Nonlinear Menggunakan Excel,” Jumlahku, vol. 1, no. 3, pp. 50–63, 2025, doi: https://doi.org/10.33222/jumlahku.v11i1.4553.
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