Abstract
This paper surveys the artificial neural networks approach. Researchers believe that these networks have the wide range of applicability, they can treat complicated problems as well. The work described here discusses an efficient computational method that can treat complicated problems. The paper intends to introduce an efficient computational method which can be applied to approximate solution of the linear two-dimensional Fredholm integral equation of the second kind. For this aim, a perceptron model based on artificial neural networks is introduced. At first, the unknown bivariate function is replaced by a multilayer perceptron neural net and also a cost function to be minimized is defined. Then a famous learning technique, namely, the steepest descent method, is employed to adjust the parameters (the weights and biases) to optimize their behavior. The article also examines application of the method which turns to be so accurate and efficient. It concludes with a survey of an example in order to investigate the accuracy of the proposed method.
Highlights
Integral equations have been extensively investigated theoretically and numerically
The paper intends to introduce an efficient computational method which can be applied to approximate solution of the linear two-dimensional Fredholm integral equation of the second kind
Alipanah and Esmaeili [2] approximated the solution of the two-dimensional Fredholm integral equation using Gaussian radial basis function based on Legendre–Gauss–Lobatto nodes and weights
Summary
Utilizing artificial neural network approach for solving two-dimensional integral equations. This article is published with open access at Springerlink.com
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