A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem

摘要

In this paper, a three-stage fifth-order Runge-Kutta method for the integration ofa special third-order ordinary differential equation (ODE) is constructed. The zero stabilityof the method is proven. The numerical study of a third-order ODE arisingin thin film flow of viscous fluid in physics is discussed. The mathematical model ofthin film flow has been solved using a new method and numerical comparisons aremade when the same problem is reduced to a first-order system of equations whichare solved using the existing Runge-Kutta methods. Numerical results have clearlyshown the advantage and the efficiency of the new method.