On the numerical solution of a driven thin film equation

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov, WENO and an upwind-type scheme, while the diffusion term is still treated implicitly. The diffusion and convection schemes are combined using a fractional step-splitting method. 2008 Elsevier Inc. All rights reserved.