Comparative Study of Secant Method and Newton-Raphson Method in Finding the Molar Volume Value of Gas Using Python

Tatik Juwariyah, Damora Rhakasywi, Syifaul Janan, Asih Melati

Abstract


Determining the molar volume of a real gas requires solving the nonlinear Van der Waals equation. This study aims to compare the efficiency and accuracy of the Newton-Raphson method and the Secant method in solving the Van der Waals equation using the Python programming language. The case study examines the determination of the molar volume of methane gas at a pressure of 56 atm and a temperature of 450 K. The comparison parameters used are the number of iterations and the speed of convergence with an error tolerance of 10⁻⁷. The results show that the Newton-Raphson method requires fewer iterations, namely 4, with a computational time of 0.00012 s. In contrast, the Secant method requires more iterations, namely 6, and a computational time of 0.00015 s. The Newton-Raphson method is less practical because it necessitates the calculation of the derivative of the function, whereas the Secant method is more practical for application in Python scripts as it only requires the calculation of the Van ders Waals equation function.


Keywords


Science; Applied Numerical Methods

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DOI: https://doi.org/10.30596/ijems.v7i2.29468

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