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Islam, A. (2015) A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods. American Journal of Computational Mathematics, 5, 393.
https://doi.org/10.4236/ajcm.2015.53034

has been cited by the following article:

• 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.