Rational Wavelets and Their Application for Solving the Heat Transfer Equations in Porous Medium
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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.
KeywordsOperational matrix Rational Bernoulli wavelets Numerical solution Porous media
Mathematics Subject Classification34K28 42C40 65L10
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.
- 8.Parand, K., Baharifard, F., Bayat Babolghani, F.: Comparison between rational Gegenbauer and modiffied generalized Laguerre functions collocation methods for solving the case of Heat transfer equations arising in porous medium. Int. J. Ind. Math. 4(2), 107–122 (2012)Google Scholar
- 9.Sohouli, A.R., Famouri, M., Kimiaeifar, A., Domairry, G.: Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux. Commun. Nonlinear Sci. Numer. Simul. 15, 1691–1699 (2010)MathSciNetCrossRefGoogle Scholar