The aim of this book is to design fast feed forward neural networks to present a method to solve singular boundary value problems for ordinary differential equations.The suggested networks use the principle of Back propagation with different training algorithms such as Levenberg–Marquardt, quasi-Newton and Bayesian regularization, update procedure then speeding suggested networks by modification these training algorithms.The Main objective of this book is to find the best training algorithm to solve singular boundary value problems. Other aim of this book, is to study the mathematical models for the equations describe the temperature variation of a spherical gas cloud under the mutual attraction of its molecules and subject to the laws of classical thermodynamics. These equations are one of the basic equations in the theory of stellar structure and have been the focus of many studies, so use the suggested networks to solve this equations. Finally, we illustrate the suggested network by solving a variety of model problems and present comparisons with solutions obtained using other different methods to show speed, accuracy and effectiveness of using the networks technique.

About the Author

Ashraf Adnan Thirthar al.qaisy I was born 14/09/1988 earned a bachelor's degree In mathematics from the University of Anbar, the year 2009 AD and then earned a master's degree In mathematics from the University of Baghdad in 2014 AD .I have a number of published papers in international journals and I participate in an international conference.

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