No abstract

a b s t r a c tThis paper intended to offer an architecture of artificial neural networks (NNs) for finding approximate solution of a second kind linear Fredholm integral equations system. For this purpose, first we substitute the N-th truncation of the Taylor expansion for unknown functions in the origin system. By applying the suggested neural network for adjusting the real coefficients of given expansions in resulting system. The proposed NN is a two-layer feedback neural network such that it can get a initial vector and then calculates it's corresponding output vector. In continuance, a cost function is defined by using output vector and the target outputs. Consequently, the reported NN using a learning algorithm that based on the gradient descent method, will adjust the coefficients in given Taylor series. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalization and high accuracy. The proposed method is illustrated by several examples with computer simulations.

Artificial neural networks (ANNs) have a large appeal to many researchers due to their feature to simulate and solve different kinds of problems that do not have algorithmic solutions. The outlined in this paper is an efficient and robust collocation method based on the ANNs and Bernstein polynomials intended for the fuzzy Abel integral equation problem. To do this, first truncated Bernstein-series polynomial of the solution function is substituted in parametric form of the given fuzzy problem. Then an architecture of ANNs namely the feed-back neural nets is designed to determine values for the unknown coefficients. Eventually, the proposed method is implemented on some numerical examples, and also is compared with an usual and classical technique.

No abstract

The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are compared with the exact solution by using computer simulations.