Open AccessSolving Mixed Volterra - Fredholm Integral Equation (MVFIE) by Designing Neural Network
Author(s) -
Al-Saif et al.,
Ameen Sh. Ameen
Publication year - 2019
Publication title -
baghdad science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.167
H-Index - 6
eISSN - 2411-7986
pISSN - 2078-8665
DOI - 10.21123/bsj.2019.16.1.0116
Subject(s) - sigmoid function , activation function , artificial neural network , transfer function , focus (optics) , mathematics , volterra integral equation , fredholm integral equation , nonlinear system , integral equation , computer science , feedforward neural network , unit (ring theory) , function (biology) , mathematical optimization , artificial intelligence , mathematical analysis , engineering , physics , quantum mechanics , electrical engineering , evolutionary biology , mathematics education , biology , optics
In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.
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