Monte Carlo Implementation on Bisection and Regula Falsi Methods for Finding Multiple Roots of Polynomial and Exponential Equations

Hery Andi Sitompul; Kristian Tarigan; Dewi Sholeha

doi:10.59086/jti.v4i2.950

Authors

Hery Andi Sitompul Universitas Darma Agung
Kristian Tarigan Universitas Darma Agung
Dewi Sholeha Universitas Darma Agung

DOI:

https://doi.org/10.59086/jti.v4i2.950

Keywords:

Keywords: Bisection, Regula Falsi, Monte Carlo, Nonlinear Equations

Abstract

Algoritma nonlinier yang tersedia dalam literatur dan pengembangan yang dilakukan oleh para ilmuwan umumnya hanya dapat menentukan satu akar persamaan nonlinier dalam satu proses perhitungan. Pengembangan metode Bagi Dua dan metode Brent dapat menentukan beberapa akar persamaan polinomial. Dengan menerapkan prinsip metode Monte Carlo pada metode Bagi Dua dan Regula Falsi, ditemukan bahwa beberapa akar persamaan nonlinier dalam bentuk polinomial atau kombinasi persamaan polinomial dan eksponensial dapat ditentukan secara akurat dalam satu proses perhitungan.

Nonlinear algorithms available in literature and developments carried out by scientists generally can only determine a single root of a nonlinear equation in a single calculation process. The development of the Bisection method and the Brent method can determine multiple roots of polynomial equations. By applying the Monte Carlo method principle to the Bisection and Regula Falsi methods, it is found that multiple roots of a nonlinear equation in polynomial form or a combination of polynomial and exponential equations can be accurately determined in a single calculation process.

References

Bouchaib Radi, Abdelhalak El Hami. 2018. Advanced Numerical Methods with Matlab, hlm.4-17. John Wiley & Sons.

Chapra, C.S. & Canale, P.R. 2010. Numerical Methods for Engineers, Sixth Edition, hlm. 164-167. McGraw Hill Companies Inc.

Bambang Agus Sulistyono, S. Sarmijo, Dian Devi Yohanie. 2024. Penerapan Metode Regula Falsi untuk Meningkatkan Akurasi Perhitungan Mekanisme Pergeseran Piston, Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, Yogyakarta.

Patrisus Batarius. 2021. Perbandingan Metode Brent dan Bisection dalam Penentuan Akar Ganda Persamaan Berbentuk Polinomial. Prosiding Seminar Nasional Riset dan Teknologi Terapan (RITEKRA). Bandung.

Gizem Temelcam, Mustafa Sivri, Inci Albayrak.2020. A New Iterative Linerazition for Solving Nonlinear Equation Syste, hlm 47-54. IJOCTA International Journal of Optimization and Control: Theories& Aplication (http://doi.org/10.11121/ijocta.01.2020.00684).

Gul Sana, Pshtiwan Othman Mohammed, Dong Yun Shin, Muhammad Aslam Noor and Mohammad Salem Oudat.2021. On Iterative Metods for Solving Nonlinear Equations in quantum Calculus. hlm 1-17. fractal and fractional. (https://doi.org/10.3390/) .

Mohammed Rassheed, Suha Shihab, Taha Rashid, Marwa Enneffati.2021. Some Step Iterative Method for Finding Roots of Non Linear Equations. hlm 95-102. Journal of Qadisiyah for Computer Science and Mathematics. Vol.13,No.1.

M Rasheed, S Shihab, O Y Mahammed and Aqeel Al-Adili.2020. Parameters Estimation of Photovoltaic Model Using Nonlinear Algorithms. ICMLAP Journals of Physics: Conference Series.( doi:10.1088/1742-6596/1795/1/012058).

Nur Hafidz, Moh Rofi, Adhi Pryanto. 2023. Penggunaan Prosedur Regula Falsi dan Interval Bagi Dua Untuk Pencarian Akar Pada Fungsi Polinomial Berderajat Tiga. SOSCIED Vol.6,No.1.

Reza Etesami, Mohsen Madadi, Mashaallah Mashinchi, Reza Ashraf Ganjoei. 2021. A New Method for Rooting equation Based On the Bisection Method, hlm 1-7. MethodsX. (https://doi.org/10.1016/j.mex.2021.101502).

Tajiyev Tahirjon Halimovich, Khusanov Azizjon Abdurashhidovich, Samijonov Azizbek Ismailjon.2022. Calculation Of The Exact Integral By The Monte Carlo Method. hlm 38-47. IJSSR Journal, Vol.11, No.12.

Tri Sutrisno. 2023. Aplikasi Penyelesaian Numerik Pencarian Akar Persamaan