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A Numerical Solution of the Urysohn-Type Fredholm İntegral Equations

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Date

2014

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Editura Academiei Romane

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Abstract

In the present paper, a combination of the Bernstein polynomials and artificial neural networks (ANNs) is presented for solving the non-linear Urysohn equation. These polynomials are utilized to reduce the solution of the given problem to the solution of a system of non-linear algebraic equations. The remaining set of nonlinear equations is solved numerically by using the ANNs approach to yield truncated Bernstein series coefficients of the solution function. Several illustrative examples with numerical simulations are provided to support the theoretical claims.

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Keywords

Approximate Solution, Artificial Neural Networks Approach, Bernstein Polynomials Method, Urysohn-Type Fredholm Integral Equation

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Citation

Jafarian, A...et al. (2014). "A Numerical Solution of the Urysohn-Type Fredholm İntegral Equations", Romanian Journal of Physics, Vol. 59, No. 7-8, pp. 625-635.

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Source

Romanian Journal of Physics

Volume

59

Issue

7-8

Start Page

625

End Page

635