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An Introduction to Neural Network Methods for Differential Equations

  • Neha Yadav
  • Anupam Yadav
  • Manoj Kumar

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Computational Intelligence book sub series (BRIEFSINTELL)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Neha Yadav, Anupam Yadav, Manoj Kumar
    Pages 1-12
  3. Neha Yadav, Anupam Yadav, Manoj Kumar
    Pages 13-15
  4. Neha Yadav, Anupam Yadav, Manoj Kumar
    Pages 17-42
  5. Neha Yadav, Anupam Yadav, Manoj Kumar
    Pages 43-100
  6. Back Matter
    Pages 101-114

About this book

Introduction

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications.

The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field.

Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.

Keywords

Cellular Neural Network Finite Element Neural Network History of Neural Networks Learning in Neural Networks Mathematical Model of Neural Network Multilayer Perceptron Neural Network Architecture Neural network methods for differential equations Radial Basis Functions Wavelet Neural Network

Authors and affiliations

  • Neha Yadav
    • 1
  • Anupam Yadav
    • 2
  • Manoj Kumar
    • 3
  1. 1.Department of Applied SciencesITM UniversityGurgaonIndia
  2. 2.Department of Sciences and HumanitiesNational Institute of Technology UttarakhandSrinagarIndia
  3. 3.Department of MathematicsMotilal Nehru National Institute of TechnologyAllahabadIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-9816-7
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-94-017-9815-0
  • Online ISBN 978-94-017-9816-7
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site
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