A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem. (6th June 2013)

• Record Type: Journal Article
• Authors: Mechee, M.; Senu, N.; Ismail, F.; Nikouravan, B.; Siri, Z.
• Other Names: Momoniat Ebrahim Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-06-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/795397
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.