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Home  >  Transactions of NAMP VOL.12

14. A NOVEL APPROACH FOR SOLVING VARIABLE COEFFICIENT INITIAL VALUE PROBLEMS USING ARTIFICIAL NEURAL NETWORKS by Okereke R.N. and Maliki O.S. Volume 12, (July – Sept., 2020 Issue)
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A NOVEL APPROACH FOR SOLVING VARIABLE COEFFICIENT INITIAL VALUE PROBLEMS USING ARTIFICIAL NEURAL NETWORKS 

Okereke R.N. and Maliki O.S.

Department of Mathematics Michael Okpara University of Agriculture Umudike, Nigeria

Abstract

A novel approach for solving ordinary differential equations with variable coefficients using Artificial Neural Networks (ANN) stems from the fact that most conventional methods of solutions rely on cumbersome weight updating to finding approximate solutions. In this paper, we develop a Neural Network algorithm using MathCAD 14 software, which enables us to slightly adjust the intrinsic biases involved in solving ordinary differential equations with variable coefficients. For this purpose, we employ a Gaussian Radial Basis Function (GRBF) to obtain the weights, which need not be adjusted, both from input layer to the hidden layer, and from the hidden layer to the output layer of the network. This also involves the use of the Statistical Package for Social Sciences (SPSS 23) software. We compare exact results with the neural network results for our example ODE problems and find the results to be in good agreement. Furthermore, this compares favourably with existing neural network methods of solution. 

Keywords: Artificial Neural Network, Weights, Biases, IVP, MathCAD 14, SPSS 23, GRBF.

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