Open AccessOn the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods
Author(s) -
A. K. Gupta,
S. Saha Ray
Publication year - 2014
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/2014/682910
Subject(s) - mathematics , haar wavelet , fisher equation , homotopy analysis method , fractional calculus , homotopy , partial differential equation , nonlinear system , exact solutions in general relativity , burgers' equation , mathematical analysis , wavelet , wavelet transform , discrete wavelet transform , pure mathematics , physics , real interest rate , quantum mechanics , artificial intelligence , computer science , monetary economics , economics , interest rate
Two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), are presented. Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. The approximate solutions thus obtained for the fractional Burgers-Fisher and generalized Fisher equations are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparison between the obtained solutions with the exact solutions exhibits that both the featured methods are effective and efficient in solving nonlinear problems. The obtained results justify the applicability of the proposed methods for fractional order Burgers-Fisher and generalized Fisher’s equations
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