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 u t + ( u 2 - u 3 ) x = - ( u 3 u xxx ) x , 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 well-known 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.