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

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{symbol} where tan φ{symbol} = d y / d x at x = x^* and plot the variation of contact angle with increasing k.