International Journal of Science, Engineering and TechnologyAuthors: Irfan Ali, Prof: Dr. Mushtaque Hussain, Dr. Kamran Mailk, Dr. Zaheer Ahmed
Abstract: This paper presents a time-dependent comparative study between numerical and analytical solutions of first-order ordinary differential equations (ODEs), with a focus on accuracy and computational performance. Numerical methods such as Taylor Method, and the classical fourth-order Runge-Kutta method are implemented and analyzed using PYTHON. The study investigates how the accuracy of each numerical method varies with time when compared to the exact analytical solution. To demonstrate this, Newton’s Law of Cooling is used as a case study, providing a real-world application where temperature changes over time are modeled by a first-order ODE. Graphical comparisons and error analyses are carried out over different time intervals to evaluate the stability and convergence behavior of each numerical method. The results reveal that while all methods can approximate the solution, the Runge-Kutta method offers the best balance of accuracy and computational efficiency. This work highlights the importance of method selection in numerical analysis and the effectiveness of PYTHON in simulating and visualizing dynamic systems.
DOI: http://doi.org/10.5281/zenodo.20765158
