A three-stage fifth-order Runge-Kutta method for directly solving special third-order differential equation with application to thin film flow problem

• Main Authors: Mechee, Mohammed, Senu, Norazak, Ismail, Fudziah, Nikouravan, B., Siri, Zailan
• Format: Article
• Language: English; English
• Published: Hindawi Publishing Corporation 2013
• Online Access: http://psasir.upm.edu.my/id/eprint/30068/1/A%20three.pdf; http://psasir.upm.edu.my/id/eprint/30068/; http://www.hindawi.com/journals/mpe/2013/795397/

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