Author(s)

Khalid Abd Elrazig Awad Alla Elnour

Department of Mathematics, Preparatory Deanship, Najran University, Najran, Kingdom of Saudi Arabia.

To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.

First-Order Differential Equations, Picard Method, Taylor Series Method, Numerical Solutions, Numerical Examples, MATLAB Software

Elnour, K. (2024) Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems. Journal of Applied Mathematics and Physics, 12, 877-896. doi: 10.4236/jamp.2024.123055.