Solving Bernoulli Differential Equations Using the Adomian Laplace Decomposition Method

Abstract

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 semi-analytical 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.