Linear Algebraic Modeling and Numerical Integration of the Fahrenheit-Celsius Conversion Function Using Simpson's Rule in Python
Keywords:
Linear Algebraic Modeling, Numerical Integration, Simpson's Rule, Scientific ComputingAbstract
This study presents a Python-based approach to model the Fahrenheit-Centigrade conversion function using linear algebraic techniques and numerically integrate the area under the curve using Simpson's Rule. By employing Python's NumPy library for linear algebra operations and numerical computations, we developed a comprehensive program to approximate the area under the curve of the conversion function. Our results demonstrate the accuracy and efficiency of the combined approach, showcasing the potential of Python for scientific computing and numerical analysis. The percentage accuracy is 100 percent, that is, both Sampson’s rule and integrated method are desirable for the estimation of area under curve of Fahrenheit to Centigrade conversion. The linear algebraic model provides a robust framework for representing the conversion function, while Simpson's Rule ensures precise numerical integration. This research contributes to the advancement of numerical methods and highlights the effectiveness of Python in solving real-world problems.
References
Atajeromavwo, E. J., Rume, E. Y., Ofyekpone, O. D., Ukpenusiohwo, D., & Ugbo, C. (2024). Python-based population forecasting for Delta State: Trapezoidal and integration method. FUDMA Journal of Sciences, 8(3), 112–118. https://doi.org/10.3303/fjs-2024-0803-2372
Cherute, C. (2023). Automation and technological solutions covering Fahrenheit to Celsius. ResearchGate. https://www.researchgate.net/publication/374194493
Davis, P. (2018). Numerical integration using Simpson’s rule: A review. Journal of Computational Mathematics, 15(1), 1–15.
Johnson, K. (2019). Analysis of linear algebraic models for temperature conversion. International Journal of Mathematics and Statistics, 18(2), 1–12.
Langtangen, H. P. (2016). A primer on scientific programming with Python (5th ed.). Springer.
Noson, S. Y. (2011). Towards a definition of an algorithm. Journal of Logic and Computation, 21(2), 253–286. https://doi.org/10.1093/logcom/exq016
Oliphant, T. E. (2007). Python for scientific computing. Computing in Science & Engineering, 9(3), 10–20.
Patel, R. (2019). Fahrenheit-centigrade conversion: A review of methods and approaches. International Journal of Research in Science and Engineering, 5(2), 123–135.
Smith, J. (2020). Automation and precision in temperature conversion functions. Journal of Metrology, 45(3), 275–290.
Smith, R. L., & Smith, R. H. (2018). Elements of environmental physics and chemistry. Routledge.
Strang, G. (2016). Introduction to linear algebra (5th ed.). Wellesley-Cambridge Press.
Taylor, R. (2017). Application of Simpson’s rule to approximate areas under curves. International Journal of Numerical Methods and Applications, 12(3), 234–245.
