Solving Second Order Non-Linear Ordinary Differential Equation Using Artificial Neural Networks.

Abstract

In This Study, We Studied On Solving A Non-Linear Ordinary Differential Equations Using Theproposed Hermite Neural Network (Henn). A Single Layer Hermite Functional Link Artifi Cial Neural Network (Henn) Developed. Henn Has No Hidden Layer And Its Input Patterndimensions Expanded By Hermite Orthogonal Polynomials. The Computations Become Ef Ficient Because The Procedure Only Requires To Be Input And Output Layers. A Feedforwardneural Networks Model And An Unsupervised Version Of Error Back Propagations Used To Min Imize The Error Function And To Update The Network Parameters. Furthermore, We Comparedthe Henn Results With The Correct Output And Results Obtained By The Well-Known Numericaltechniques(Rk4). Two Examples And One Implementation (Van Der Pol?��?Duffing Oscilla Tor Equation) Took To Show The Efficiency And Power Of This Developed Model With Plottedgraphs Using Python Code.