A Study on Some Numerical Methods for Simulating Mathematical Models of Ordinary Differential Equations

Abstract

Study’s Excerpt:
• The study evaluates numerical methods for ODEs to guide suitable model simulations.
• Adomian Decomposition suits decay/growth models; block method excels in all problems, including SIR.
• The study highlights numerical methods' ease and precision in simulating mathematical models.
Full Abstract:
This study presents a comparative analysis on some numerical methods for simulating mathematical models of ordinary differential equations, including Euler, Classical Runge-Kutta, Adomian Decomposition, Block, and Simulink. We examine each method's accuracy, stability, and consistency through a series of test cases. These methods are applied to simulate some selected mathematical models, and the results are shown in tables. The graph of each table is depicted in figures for discussion and comparative analysis. The results show that, while straightforward, the Euler method demonstrates significant limitations in accuracy compared to the Classical Runge-Kutta method, which provides reliable and precise results. The Adomian Decomposition Method solves the problems and yields results very close to the analytical solution, but the block method performs better due to its multistep approach. Simulink offers a more robust approach for modelling and simulation with visible and interpretable solutions for good understanding. This study revealed that numerical methods can easily be used to better simulate mathematical models that may not have analytical solutions and thus provide approximate solutions.