Browsing by Author "Nia, Safa Measoomy"

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Citation Count: Jafarian, Ahmad...et al. (2013). "Numerical solution of linear integral equations system using the Bernstein collocation method", Advances In Difference Equations.
Numerical Solution of Linear Integral Equations System Using the Bernstein Collocation Method
(Springer International Publishing AG, 2013) Jafarian, Ahmad; Nia, Safa Measoomy; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
Since in some application mathematical problems finding the analytical solution is too complicated, in recent years a lot of attention has been devoted by researchers to find the numerical solution of this equations. In this paper, an application of the Bernstein polynomials expansion method is applied to solve linear second kind Fredholm and Volterra integral equations systems. This work reduces the integral equations system to a linear system in generalized case such that the solution of the resulting system yields the unknown Bernstein coefficients of the solutions. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.
Citation Count: Jafarian, Ahmad...et al. (2018). "On artificial neural networks approach with new cost functions", Applied Mathematics and Computation, Vol. 339, pp. 546-555.
On artificial neural networks approach with new cost functions
(Elsevier Science INC, 2018) Jafarian, Ahmad; Nia, Safa Measoomy; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
In this manuscript, the artificial neural networks approach involving generalized sigmoid function as a cost function, and three-layered feed-forward architecture is considered as an iterative scheme for solving linear fractional order ordinary differential equations. The supervised back-propagation type learning algorithm based on the gradient descent method, is able to approximate this a problem on a given arbitrary interval to any desired degree of accuracy. To be more precise, some test problems are also given with the comparison to the simulation and numerical results given by another usual method. (C) 2018 Elsevier Inc. All rights reserved.
On Bernstein Polynomials Method to the System of Abel Integral Equations
(Hindawi LTD, 2014) Jafarian, A.; Nia, Safa Measoomy; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.