Oscillations of solutions of initial value problems for parabolic equations by the decomposition method

Abstract

In this paper we study an analytic solution and a reliable numerical approximation of a linear and nonlinear parabolic equations by using the Adomian's decomposition method. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equations. Comparing the numerical results with their exact numerical results, they show that the present approach is relatively easy and highly accurate.