A NEW APPROACH TO SOLVE BLASIUS EQUATION USING PARAMETER IDENTIFICATION OF NONLINEAR FUNCTIONS BASED ON THE BEES ALGORITHM (BA)

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.

[1]  M. Rockstein.  Bees. Their Vision, Chemical Senses, and Language , 1952 .

[2]  R. Morse.  Bees, Their Vision, Chemical Senses and Language , 1973 .

[3]  Hyuk Lee,et al.  Neural algorithm for solving differential equations , 1990 .

[4]  Andrew J. Meade,et al.  The numerical solution of linear ordinary differential equations by feedforward neural networks , 1994 .

[5]  T. Seeley.  The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies , 1995 .

[6]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[7]  Guy Theraulaz,et al.  Self-Organization in Biological Systems , 2001, Princeton studies in complexity.

[8]  Duc Truong Pham,et al.  APPLICATION OF THE BEES ALGORITHM TO THE TRAINING OF RADIAL BASIS FUNCTION NETWORKS FOR CONTROL CHART PATTERN RECOGNITION , 2006 .

[9]  Alaeddin Malek,et al.  Numerical solution for high order differential equations using a hybrid neural network - Optimization method , 2006, Appl. Math. Comput..

[10]  Zong-Yi Lee,et al.  Method of bilaterally bounded to solution blasius equation using particle swarm optimization , 2006, Appl. Math. Comput..

[11]  D. Pham,et al.  THE BEES ALGORITHM, A NOVEL TOOL FOR COMPLEX OPTIMISATION PROBLEMS , 2006 .

[12]  I. Qureshi,et al.  SWARM INTELLIGENCE FOR THE PROBLEM OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS AND ITS APPLICATION TO WELL-KNOWN WESSINGER'S EQUATION , 2009 .

[13]  Afshin Ghanbarzadeh,et al.  ASSESSMENT OF ELECTRICITY DEMAND IN IRAN'S INDUSTRIAL SECTOR USING DIFFERENT INTELLIGENT OPTIMIZATION TECHNIQUES , 2011, Appl. Artif. Intell..

[14]  A. Ghanbarzadeh,et al.  Total Energy Demand Estimation in Iran Using Bees Algorithm , 2011 .

[15]  M. A. Behrang,et al.  Using Bees Algorithm and Artificial Neural Network to Forecast World Carbon Dioxide Emission , 2011 .

[16]  A. Ghanbarzadeh,et al.  New sunshine-based models for predicting global solar radiation using PSO (particle swarm optimizati , 2011 .