TITLE:
Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems
AUTHORS:
Khalid Abd Elrazig Awad Alla Elnour
KEYWORDS:
First-Order Differential Equations, Picard Method, Taylor Series Method, Numerical Solutions, Numerical Examples, MATLAB Software
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.3,
March
29,
2024
ABSTRACT: 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.