摘要
A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solu- tions of the nonlinear second-order ODE are investigated us- ing finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order non- linear ODE is shown to converge faster than a finite differ- ence formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numeri- cal solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.
A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solu- tions of the nonlinear second-order ODE are investigated us- ing finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order non- linear ODE is shown to converge faster than a finite differ- ence formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numeri- cal solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.
