Evolutionary computing for nonlinear singular boundary value problems using neural network, genetic algorithm and active-set algorithm

2021 ◽  
Vol 136 (2) ◽  
Author(s):  
Zulqurnain Sabir ◽  
Chaudry Masood Khalique ◽  
Muhammad Asif Zahoor Raja ◽  
Dumitru Baleanu
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Evolutionary Computing ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Active Set ◽  
Active Set Algorithm

scholarly journals Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Luma N. M. Tawfiq ◽  
Ashraf A. T. Hussein
Keyword(s):  
Neural Network ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Back Propagation ◽  
Singular Boundary ◽  
Training Algorithms ◽  
Singular Boundary Value Problems ◽  
Feed Forward Neural Network ◽  
Feed Forward ◽  
The Neural Networks

The aim of this paper is to design feed forward neural network for solving second-order singular boundary value problems in ordinary differential equations. The neural networks use the principle of back propagation with different training algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian Regulation. Two examples are considered to show that effectiveness of using the network techniques for solving this type of equations. The convergence properties of the technique and accuracy of the interpolation technique are considered.

scholarly journals A Galerkin method ofO(h2)for singular boundary value problems

2002 ◽  
Vol 29 (6) ◽  
pp. 361-369
Author(s):  
G. K. Beg ◽  
M. A. El-Gebeily
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Basis Functions ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Special Basis

We describe a Galerkin method with special basis functions for a class of singular two-point boundary value problems. The convergence is shown which is ofO(h2)for a certain subclass of the problems.

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