Stručni rad

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 ; Veleučilište suvremenih informacijskih tehnologija u Zagrebu, Klaićeva 7, Zagreb, Hrvatska *
Marijan Čančarević ; Veleučilište suvremenih informacijskih tehnologija u Zagrebu, Klaićeva 7, Zagreb, Hrvatska *
Ivica Čulina ; Veleučilište Velika Gorica, Zagrebačka 5,Velika Gorica, Hrvatska *

* Dopisni autor.

Sažetak

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.

Ključne riječi

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

Hrčak ID:

335818

URI

https://hrcak.srce.hr/335818

Datum izdavanja:

2.6.2025.

Posjeta: 243 *