On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods
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 appro...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/682910 |
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| _version_ | 1832549829619744768 |
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| author | A. K. Gupta S. Saha Ray |
| author_facet | A. K. Gupta S. Saha Ray |
| author_sort | A. K. Gupta |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e9a6bd19e10449bb86336dd215e08a64 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e9a6bd19e10449bb86336dd215e08a642025-02-03T06:08:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/682910682910On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable MethodsA. K. Gupta0S. Saha Ray1Department of Mathematics, National Institute of Technology, Rourkela 769008, IndiaDepartment of Mathematics, National Institute of Technology, Rourkela 769008, IndiaTwo 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.http://dx.doi.org/10.1155/2014/682910 |
| spellingShingle | A. K. Gupta S. Saha Ray On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods International Journal of Mathematics and Mathematical Sciences |
| title | On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods |
| title_full | On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods |
| title_fullStr | On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods |
| title_full_unstemmed | On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods |
| title_short | On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods |
| title_sort | on the solutions of fractional burgers fisher and generalized fisher s equations using two reliable methods |
| url | http://dx.doi.org/10.1155/2014/682910 |
| work_keys_str_mv | AT akgupta onthesolutionsoffractionalburgersfisherandgeneralizedfishersequationsusingtworeliablemethods AT ssaharay onthesolutionsoffractionalburgersfisherandgeneralizedfishersequationsusingtworeliablemethods |