Professional paper

https://doi.org/10.19279/TVZ.PD.2024-12-4-15

EULER AND PICARD METHODS FOR SOLVING FIRST-ORDER DIFFERENTIAL EQUATIONS – CLASSICAL AND SOFTWARE-BASED

Edmond Krusha ; College for Information Technology, Klaićeva 7, Zagreb, Croatia *
Marijan Čančarević ; College for Information Technology, Klaićeva 7, Zagreb, Croatia *
Ivica Čulina ; University of Applied Sciences Velika Gorica, Zagrebačka 5, Velika Gorica, Croatia *

* Corresponding author.

Abstract

This paper describes and demonstrates the algorithms of Euler's and Picard's methods for solving first-order differential equations using a specific example. Both methods provide approximate solutions, with Euler's method [1], [3] yielding a numerical solution while Picard's method [2] initially provides an analytical solution, which can then be transformed into a numerical solution through direct substitution if necessary. The selected example illustrates these algorithms both through the classical solution approach and by utilizing the SageMath software [4]. The primary objective of this study is to highlight the advantages of numerical methods, particularly when modern technologies are employed.

Keywords

numerical method; differential equation; Euler; Picard; software; SageMath

Hrčak ID:

335818

URI

https://hrcak.srce.hr/335818

Publication date:

2.6.2025.

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