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−ky‴=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−ky‴=y−k. We show that the domain of convergence of the Adomian decomposition solution is dependent on kk. We truncate the Adomian decomposition solution at a suitable order to ensure that the truncated solution satisfies the contact line condition, y=0y=0, at some point x=x∗x=x∗. We then determine the contact angle ϕϕ where tanϕ=dy/dx at x=x∗x=x∗ and plot the variation of contact angle with increasing kk.