A Hybrid Neural Network and Gravitational Search Algorithm (HNNGSA) Method to Solve well known Wessinger's Equation
This study presents a hybrid neural network and Gravitational Search Algorithm (HNGSA) method to solve well known Wessinger's equation. To aim this purpose, gravitational search algorithm (GSA) technique is applied to train a multi-layer perceptron neural network, which is used as approximation solution of the Wessinger's equation. A trial solution of the differential equation is written as sum of two parts. The first part satisfies the initial/ boundary conditions and does not contain any adjustable parameters and the second part which is constructed so as not to affect the initial/boundary conditions. The second part involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. In order to demonstrate the presented method, the obtained results of the proposed method are compared with some known numerical methods. The given results show that presented method can introduce a closer form to the analytic solution than other numerical methods. Present method can be easily extended to solve a wide range of problems.
Neural Networks, Gravitational Search Algorithm
(GSR), Wessinger's Equation.
A New Solution for Natural Convection of Darcian Fluid about a Vertical Full Cone Embedded in Porous Media Prescribed Wall Temperature by using a Hybrid Neural Network-Particle Swarm Optimization Method
Fluid flow and heat transfer of vertical full cone
embedded in porous media is studied in this paper. Nonlinear
differential equation arising from similarity solution of inverted cone
(subjected to wall temperature boundary conditions) embedded in
porous medium is solved using a hybrid neural network- particle
swarm optimization method.
To aim this purpose, a trial solution of the differential equation is
defined as sum of two parts. The first part satisfies the initial/
boundary conditions and does contain an adjustable parameter and
the second part which is constructed so as not to affect the
initial/boundary conditions and involves adjustable parameters (the
weights and biases) for a multi-layer perceptron neural network.
Particle swarm optimization (PSO) is applied to find adjustable
parameters of trial solution (in first and second part). The obtained
solution in comparison with the numerical ones represents a
Porous Media, Ordinary Differential Equations
(ODE), Particle Swarm Optimization (PSO), Neural Network (NN).
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.
Bees Algorithm (BA); Approximate Solutions;
Blasius Differential Equation.