Numerical approximation of Newell-Whitehead-Segel equation of fractional order
The aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-06-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2015-0032 |
| _version_ | 1829496381872537600 |
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| author | Kumar Devendra Sharma Ram Prakash |
| author_facet | Kumar Devendra Sharma Ram Prakash |
| author_sort | Kumar Devendra |
| collection | DOAJ |
| description | The aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order. |
| first_indexed | 2024-12-16T07:30:03Z |
| format | Article |
| id | doaj.art-f275dcc62df9465181af251d903b33f7 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-16T07:30:03Z |
| publishDate | 2016-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-f275dcc62df9465181af251d903b33f72022-12-21T22:39:22ZengDe GruyterNonlinear Engineering2192-80102192-80292016-06-0152818610.1515/nleng-2015-0032Numerical approximation of Newell-Whitehead-Segel equation of fractional orderKumar Devendra0Sharma Ram Prakash1Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, IndiaDepartment of Mathematics, JECRC University, Jaipur-303905, Rajasthan, IndiaThe aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order.https://doi.org/10.1515/nleng-2015-0032fractional newell-whitehead-segel equationstripe patterncaputo fractional derivativehomotopy analysis methodsumudu transform |
| spellingShingle | Kumar Devendra Sharma Ram Prakash Numerical approximation of Newell-Whitehead-Segel equation of fractional order Nonlinear Engineering fractional newell-whitehead-segel equation stripe pattern caputo fractional derivative homotopy analysis method sumudu transform |
| title | Numerical approximation of Newell-Whitehead-Segel equation of fractional order |
| title_full | Numerical approximation of Newell-Whitehead-Segel equation of fractional order |
| title_fullStr | Numerical approximation of Newell-Whitehead-Segel equation of fractional order |
| title_full_unstemmed | Numerical approximation of Newell-Whitehead-Segel equation of fractional order |
| title_short | Numerical approximation of Newell-Whitehead-Segel equation of fractional order |
| title_sort | numerical approximation of newell whitehead segel equation of fractional order |
| topic | fractional newell-whitehead-segel equation stripe pattern caputo fractional derivative homotopy analysis method sumudu transform |
| url | https://doi.org/10.1515/nleng-2015-0032 |
| work_keys_str_mv | AT kumardevendra numericalapproximationofnewellwhiteheadsegelequationoffractionalorder AT sharmaramprakash numericalapproximationofnewellwhiteheadsegelequationoffractionalorder |