The fluid dynamical behaviour of thin liquid films, whether forced to spread over a solid surface or deposited/printed as a distinct pattern, is of enormous significance to manufacturing industry and practice. Such flows involve the presence of a free surface, dynamic wetting and interfacial phenomena such as surface tension gradients, each of which represents a considerable challenge in its own right. This paper describes the development and application of a novel, fast, state-of-the-art numerical algorithm for the solution of a particular class of governing fluid flow equations, generic to these types of free surface problem.