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

✍ Scribed by E. Momoniat; T.A. Selway; K. Jina

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 248 KB
• Volume: 66
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.03.021

✦ Synopsis

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 = dy/dx at x = x * and plot the variation of contact angle with increasing k.