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All Journal Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam
Naufal Afi Adani
Department of Mathematics Education, Faculty of Tarbiyah, Universitas Islam Negeri Raden Mas Said Surakarta, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Comparison of the Newton–Raphson and Secant Methods in a Simple Pendulum Model Naufal Afi Adani; Anindhita Maheswari; Ari Wibowo
Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam Vol. 23 No. 1 (2026): Sainmatika : Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam
Publisher : Universitas PGRI Palembang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31851/sainmatika.v23i1.21526

Abstract

Various problems in mathematics and physics, including the nonlinear pendulum model, cannot be solved analytically, so numerical methods are used to obtain approximate solutions with a certain error tolerance. This study compares the Newton–Raphson and Secant methods in solving nonlinear equations in a pendulum system based on iteration count, error, and convergence stability using a comparative quantitative approach.  The results show that neither method is absolutely superior, as both successfully produced approximate solutions. The value of θ (angular displacement) decreases as the pendulum length (L) increases due to the proportional relationship involving potential energy and the factor mgL. The Newton–Raphson method reached the solution in 4 iterations, while the Secant method required 4–6 iterations. The average order of convergence for Newton–Raphson approaches p ≈ 2 (quadratic), whereas the Secant method approaches p ≈ 1.62 (superlinear). The differences between the two methods are more influenced by the choice of initial guesses and the respective mechanisms of each method.
Co-Authors Anindhita Maheswari Ari Wibowo