Dorrah, Azis and Tiryono, Tiryono and Agus Sutrisno, agus and Misgiyati, Misgiyati and Ilma Isyahna Sholeha, Isyahna (2025) Solving Bernoulli Differential Equations Using the Adomian Laplace Decomposition Method. International Journal of Advance Social Sciences and Education (IJASSE), 3 (1). pp. 59-72. ISSN 2988-2133

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Abstract

Differential Equation, Adomian Laplace, Decomposition Method Received: 19, December Revised: 20, January Accepted: 28, February ©2025 Azis, Tiryono, Sutrisno, Sholeha, Misgiyati: This is an open-access article distributed under the terms of the Creative Commons Atribusi 4.0 Internasional. Bernoulli differential equation is one form of first order ordinary differential equation. Because Bernoulli differential equation is a non-linear equation with a fairly complex form, this study uses the Adomian Laplace decomposition method to find its solution. This method is a semianalytical method that combines the Laplace transform and the Adomian decomposition method. The steps for solving it include applying the Laplace transform to the Bernoulli differential equation, defining the solution as an infinite series, using the Adomian polynomial to solve the non-linear part, and applying the inverse Laplace transform. The simulation results and error analysis show that the Adomian Laplace decomposition method can provide an accurate approach to the exact solution for values 0 ≤ t ≤ 0.2. Meanwhile, for values t ≥ 0.2 the resulting solution tends to move away from the exact solution.

Item Type:	Article
Subjects:	Q Science > QA Mathematics > QA76 Computer software
Divisions:	Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User:	AGUS SUTRI
Date Deposited:	13 Jun 2025 11:25
Last Modified:	13 Jun 2025 11:25
URI:	http://repository.lppm.unila.ac.id/id/eprint/54622

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