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

M. Mechee, N. Senu, F. Ismail, B. Nikouravan and Z. Siri

Mathematical Problems in Engineering, 2013, vol. 2013, 1-7

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:795397

DOI: 10.1155/2013/795397

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