A note on Laplace Adomian decomposition method on a linear problem

Manzo Senjaya Budiman; Daniel Salim

doi:10.62918/hjma.v2i1.16

Authors

Manzo Senjaya Budiman Universitas Katolik Parahyangan
Daniel Salim Universitas Katolik Parahyangan

DOI:

https://doi.org/10.62918/hjma.v2i1.16

Keywords:

Ordinary differential equation, Initial value problem, Laplace Adomian decomposition method

Abstract

In last two decades, Laplace Adomian Decomposition Method (LADM) is vastly used to solve non-linear (or even fractional order) differential equations. The method approaches the solution with the partial sums of function series. However, it is not easy to show that the limit of the function series is the exact solution of the problem. In this article, we consider a simple problem such as homogenous second-order linear ordinary differential equation with constant coefficients. We prove analytically that the LADM gives the right exact solution to the considered problem.

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