Track: Graduate Student Paper Competition

Abstract

Adomian decomposition method is a numerical method that introduced by George Adomian to solve stochastic equations. This method be able to solve equations without linearization, discretization, perturbation or other restrictive assumptions. This method can also be used to solve differential equations with integer or fractional order, ordinary or partial, with initial value or boundary problems, with variable or constant coefficients, linear or nonlinear, homogeneous or nonhomogeneous. Thus, the purpose of this paper is to review the application of the Adomian decomposition method to find solutions for various equations. For example ordinary and partial differential equations, also those with fractional order. There is also a review of the Adomian decomposition method developed with Laplace transformation. Heat and Black-Scholes equations can also be easily solved by this decomposition method. The results show that the Adomian decomposition method is an effective and easy algorithm to solve various differential equations.