On the solution of the fourth order parabolic equation by the decomposition method

Abstract

In this paper, the fourth order parabolic partial differential equation, that governs the behavior of a vibrating beam, is solved by using the Adomian Decomposition Method. The solution is derived in the form of a power series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling "noise" terms whose sum vanishes in the limit. Comparing this methodology with some known techniques shows that the present approach is highly accurate.