Application of He's Variational Iterative Method for Solving Thin Film Flow Problem Arising in Non-Newtonian Fluid Mechanics
作者： Abdul M. Siddiqui , Ali A. Farooq , Tahira Haroon , Muhammad A. Rana , Bruce S. Babcock
关键词: Thin film flow 、 Adomian decomposition method 、 Inclined plane 、 Nonlinear boundary value problem 、 Nonlinear system 、 Decomposition method (constraint satisfaction) 、 Iterative method 、 Mathematical optimization 、 Mathematics 、 Applied mathematics 、 Non-Newtonian fluid
摘要: In this paper, He’s variational iteration method is successfully employed to solve a nonlinear boundary value problem arising in the study of thin film flow third grade fluid down an inclined plane. For comparison, same solved by Adomian decomposition method. The results show that difference between two solutions negligible. conclusion technique may be considered alternative and efficient for finding approximate both linear problems. Furthermore, has advantage over it solves problems without using polynomials.
harvard.edu
researchgate.net 
sci-hub.st 参考文章(15)
Necdet Bildik, Ali Konuralp, Two-dimensional differential transform method, Adomian's decomposition method, and variational iteration method for partial differential equations International Journal of Computer Mathematics. ,vol. 83, pp. 973- 987 ,(2006) , 10.1080/00207160601173407
Ji-Huan He, Variational iteration method-Some recent results and new interpretations Journal of Computational and Applied Mathematics. ,vol. 207, pp. 3- 17 ,(2007) , 10.1016/J.CAM.2006.07.009
Ji-Huan He, Homotopy perturbation technique Computer Methods in Applied Mechanics and Engineering. ,vol. 178, pp. 257- 262 ,(1999) , 10.1016/S0045-7825(99)00018-3
George Adomian, Solving Frontier Problems of Physics: The Decomposition Method ,(1993)
A.M. Siddiqui, R. Mahmood, Q.K. Ghori, Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane Chaos Solitons & Fractals. ,vol. 35, pp. 140- 147 ,(2008) , 10.1016/J.CHAOS.2006.05.026
Shijun Liao, SA Sherif, Beyond Perturbation: Introduction to the Homotopy Analysis Method ,(2003)
Ji-Huan He, Variational iteration method – a kind of non-linear analytical technique: some examples International Journal of Non-linear Mechanics. ,vol. 34, pp. 699- 708 ,(1999) , 10.1016/S0020-7462(98)00048-1
G Adomian, A review of the decomposition method in applied mathematics Journal of Mathematical Analysis and Applications. ,vol. 135, pp. 501- 544 ,(1988) , 10.1016/0022-247X(88)90170-9
Mustafa Inc, Ebru Cavlak, On numerical solutions of a new coupled MKdV system by using the Adomian decomposition method and He's variational iteration method Physica Scripta. ,vol. 78, pp. 045008- ,(2008) , 10.1088/0031-8949/78/04/045008
A.M. Siddiqui, M. Hameed, B.M. Siddiqui, Q.K. Ghori, Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid Communications in Nonlinear Science and Numerical Simulation. ,vol. 15, pp. 2388- 2399 ,(2010) , 10.1016/J.CNSNS.2009.05.073