Author:
Vinodbhai Chavda Divyesh,Dubey Shruti
Abstract
AbstractIn this paper, an efficient orthogonal neural network (ONN) approach is introduced to solve the higher-order neutral delay differential equations (NDDEs) with variable coefficients and multiple delays. The method is implemented by replacing the hidden layer of the feed-forward neural network with the orthogonal polynomial-based functional expansion block, and the corresponding weights of the network are obtained using an extreme learning machine(ELM) approach. Starting with simple delay differential equations (DDEs), an interest has been shown in solving NDDEs and system of NDDEs. Interest is given to consistency and convergence analysis, and it is seen that the method can produce a uniform closed-form solution with an error of order$$2^{-n}$$2-n, wherenis the number of neurons. The developed neural network method is validated over various types of example problems(DDEs, NDDEs, and system of NDDEs) with four different types of special orthogonal polynomials.
Funder
Ministry of Education, India
Indian Institute of Technology Madras
Publisher
Springer Science and Business Media LLC
Cited by
4 articles.
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