A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem-Reference-Cited by-同舟云学术

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

Published:2013 Issue: Volume:2013 Page:1-7
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Mechee M.¹²,Senu N.³,Ismail F.³,Nikouravan B.⁴,Siri Z.¹

Affiliation:

1. Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

2. Department of Mathematics, Faculty of Mathematics and Computer Sciences, University of Kufa, Najaf, Iraq

3. Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

4. Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

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.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2013/795397.pdf

Reference21 articles.

1. A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations

2. Solving second order initial value problems by a hybrid multistep method without predictors

3. A class of hybrid collocation methods for third-order ordinary differential equations

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