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National Academy Science Letters

, Volume 38, Issue 5, pp 425–428 | Cite as

Numerical Solution of Bratu’s Problem Using Multilayer Perceptron Neural Network Method

  • Manoj Kumar
  • Neha YadavEmail author
Short Communication

Abstract

In this article, an artificial neural network (ANN) method is presented to obtain the closed analytic form of the one dimensional Bratu type equations, which are widely applicable in fuel ignition of the combustion theory and heat transfer. Our goal is to provide optimal solution of Bratu type equations with reduced calculus effort using ANN method in comparison to the other existing methods. Various test cases have been simulated using proposed neural network model and the accuracy has been substantiated by considering a large number of simulation data for each model with enough independent runs. Numerical results show that this method has potentiality to become an efficient approach for solving Bratu’s problems with less computing time and memory space.

Keywords

Artificial neural network Back propagation algorithm Bratu’s equations Levenberg–Marquardt algorithm Conjugate gradient algorithm 

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Copyright information

© The National Academy of Sciences, India 2015

Authors and Affiliations

  1. 1.Department of MathematicsMotilal Nehru National Institute of TechnologyAllahabadIndia
  2. 2.Department of Applied ScienceITM UniversityGurgaonIndia

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