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Rational Wavelets and Their Application for Solving the Heat Transfer Equations in Porous Medium

  • P. Rahimkhani
  • Y. Ordokhani
Original Paper
  • 30 Downloads

Abstract

In this paper, a new approach is presented for solving natural convection heat transfer equations embedded in porous medium. These equations are non-linear, three-point boundary value equations on semi-infinite interval. Our approach is based upon the rational Bernoulli wavelets; these wavelets are first introduced. Then the derivative operational matrix of rational Bernoulli wavelets is given. This matrix is utilized to reduce the solution of the under study problem to a system of algebraic equations. Error estimation of our approximation is provided. We also present the comparison of this work with Runge–Kutta method and other methods, moreover, in the figure of the relative errors, we show that our results are accurate and applicable.

Keywords

Operational matrix Rational Bernoulli wavelets Numerical solution Porous media 

Mathematics Subject Classification

34K28 42C40 65L10 

Notes

Acknowledgements

The first author is supported by the national elites foundation. Authors are very grateful to one of the reviewers for carefully reading the paper and for his(her) comments and suggestions which have improved the paper.

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Copyright information

© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesAlzahra UniversityTehranIran

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