Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
A New Approach to Solve Blasius Equation using Parameter Identification of Nonlinear Functions based on the Bees Algorithm (BA)

Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

Abstract:

In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082393

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1432

References:


[1] A. Malek, R.S. Beidokhti, Numerical solution for high order differential equations using a hybrid neural networkÔÇöOptimization method. Applied Mathematics and Computation. 2006; 183: 260-271.
[2] H. Lee, I.S. Kang, Neural algorithms for solving differential equations, Journal of Computational Physics 1990; 91: 110-131.
[3] A.J. Meade Jr, A.A. Fernandez, The numerical solution of linear ordinary differential equations by feedforward neural networks, Mathematical and Computer Modelling. 1994; 19 (12): 1-25.
[4] I.E. Lagris, A. Likas, D.I. Fotiadis. Artificial neural networks for solving ordinary and partitial differential equations. IEEE Transactions on Neural Networks. 1998; 9 (5): 987-1000.
[5] J.A. Khan, R.M.A. Zahoor, I.M. Qureshi, Swarm intelligence for the problem of non-linear ordinary differential equations and its application to well known Wessinger's equation. European Journal of scientific research. 2009; 34(4): 514-525.
[6] Z.Y. Lee, Method of bilaterally bounded to solution blasius equation using particle swarm optimization. Applied Mathematics and Computation 2006; 179: 779-786.
[7] Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi M. Technical Note: Bees Algorithm. Cardiff: Cardiff University, Manufacturing Engineering Centre; 2005.
[8] Von Frisch K. Bees: Their Vision, Chemical Senses and Language. Revised Edition ed. NY: Ithaca, Cornell University Press; 1976.
[9] Seeley TD. The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies. Cambridge, Massachusetts: Harvard University Press; 1996.
[10] Camazine S, Deneubourg JL, Franks NR, Sneyd J, Theraulaz G, Bonabeau E. Self-Organization in Biological Systems. Princeton: Princeton University Press; 2003.
[11] Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence: from Natural to Artificial Systems. New York: Oxford University Press; 1999.
[12] Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi M. The Bees Algorithm, A Novel Tool for Complex Optimisation Problems. in 2nd Int Virtual Conf on Intelligent Production Machines and Systems (IPROMS);2006, pp.454-459.
[13] Pham DT, Ghanbarzadeh A, Koc E, Otri S. Application of the Bees Algorithm to the Training of Radial Basis Function Networks for Control Chart Pattern Recognition. in 5th CIRP International Seminar on Intelligent Computation in Manufacturing Engineering (CIRP ICME '06). Ischia, Italy; 2006, pp. 711-716.
[14] M.A.Behrang, E.Assareh, M.R.Assari, A.Ghanbarzadeh, Total energy demand estimation in Iran using Bees Algorithm. Energy Sources, Part B: Economics, Planning, and Policy. Accepted. DOI: 10.1080/15567240903502594.
[15] Using Bees Algorithm and Artificial Neural Network to Forecast World Carbon Dioxide Emission. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects. Accepted. DOI: 10.1080/15567036.2010.493920.
[16] E. Assareh, M.A.Behrang, M.R.Assari, A.Ghanbarzadeh. Application of particle swarm optimization (PSO) and genetic algorithm (GA) techniques on demand estimation of oil in Iran. Energy 35 (2010) 5223- 5229.
[17] M.A. Behrang., E. Assareh, M.R. Assari, M.R., and A. Ghanbarzadeh. Assessment of electricity demand in Iran's industrial sector using different intelligent optimization techniques. Applied Artificial Intelligence 2011; 25: 292-304. doi:10.1080/08839514.2011.559572
[18] M.A. Behrang, E. Assareh, A.R. Noghrehabadi, and A. Ghanbarzadeh. New sunshine-based models for predicting global solar radiation using PSO (particle swarm optimization) technique. Energy 2011; 36: 3036- 3049. doi:10.1016/j.energy.2011.02.048.