Analysis of Adomian decomposition applied to a third-order ordinary differential equation from thin film flow

Abstract

The Adomian decomposition method is applied to the third-order ordinary differential equation y ‴ = y − k obtained by considering a travelling wave solution admitted by a generalized thin film equation or for thin film flow down a vertical wall. The Adomian decomposition method leads to a power series approximation to the solution of y ‴ = y − k . We show that the domain of convergence of the Adomian decomposition solution is dependent on k . We truncate the Adomian decomposition solution at a suitable order to ensure that the truncated solution satisfies the contact line condition, y = 0 , at some point x = x ∗ . We then determine the contact angle ϕ where tan ϕ = d y / d x at x = x ∗ and plot the variation of contact angle with increasing k .