Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method
In this article, the approximate analytical solution of the time-fractional Cahn–Hilliard equation with quadratic form of the source/sink term is obtained using the powerful homotopy analysis method, which permits us to select a convergence control parameter that minimizes residual errors. The conce...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Published: |
SAGE Publications Inc
2017
|
| Subjects: |
| _version_ | 1796961715240304640 |
|---|---|
| author | Tripathi, Neeraj Kumar Das, Subir Ong, Seng Huat Jafari, Hossein Al Qurashi, Maysaa’ Mohamed |
| author_facet | Tripathi, Neeraj Kumar Das, Subir Ong, Seng Huat Jafari, Hossein Al Qurashi, Maysaa’ Mohamed |
| author_sort | Tripathi, Neeraj Kumar |
| collection | UM |
| description | In this article, the approximate analytical solution of the time-fractional Cahn–Hilliard equation with quadratic form of the source/sink term is obtained using the powerful homotopy analysis method, which permits us to select a convergence control parameter that minimizes residual errors. The concerned method is more general in theory and widely valid in practice to solve nonlinear problems even for fractional order systems as it provides a convenient way to guarantee the convergence of the approximate series. The results have been given to show the effect of the reaction term on the solution profile in both fractional and standard order cases for different particular cases. The main feature of this study is the authentication that only a few iterations are required to obtain the accurate approximate solution of the present mathematical model. This is justified through error analysis for both fractional and standard order cases. This striking feature of savings in time is exhibited through graphical presentations of the numerical values when the system passes from standard order to fractional order in the presence or absence of the reaction term. |
| first_indexed | 2024-03-06T05:58:15Z |
| format | Article |
| id | um.eprints-22874 |
| institution | Universiti Malaya |
| last_indexed | 2024-03-06T05:58:15Z |
| publishDate | 2017 |
| publisher | SAGE Publications Inc |
| record_format | dspace |
| spelling | um.eprints-228742019-10-26T07:09:23Z http://eprints.um.edu.my/22874/ Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method Tripathi, Neeraj Kumar Das, Subir Ong, Seng Huat Jafari, Hossein Al Qurashi, Maysaa’ Mohamed QA Mathematics In this article, the approximate analytical solution of the time-fractional Cahn–Hilliard equation with quadratic form of the source/sink term is obtained using the powerful homotopy analysis method, which permits us to select a convergence control parameter that minimizes residual errors. The concerned method is more general in theory and widely valid in practice to solve nonlinear problems even for fractional order systems as it provides a convenient way to guarantee the convergence of the approximate series. The results have been given to show the effect of the reaction term on the solution profile in both fractional and standard order cases for different particular cases. The main feature of this study is the authentication that only a few iterations are required to obtain the accurate approximate solution of the present mathematical model. This is justified through error analysis for both fractional and standard order cases. This striking feature of savings in time is exhibited through graphical presentations of the numerical values when the system passes from standard order to fractional order in the presence or absence of the reaction term. SAGE Publications Inc 2017 Article PeerReviewed Tripathi, Neeraj Kumar and Das, Subir and Ong, Seng Huat and Jafari, Hossein and Al Qurashi, Maysaa’ Mohamed (2017) Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method. Advances in Mechanical Engineering, 9 (12). p. 168781401774077. ISSN 1687-8132, DOI https://doi.org/10.1177/1687814017740773 <https://doi.org/10.1177/1687814017740773>. https://doi.org/10.1177/1687814017740773 doi:10.1177/1687814017740773 |
| spellingShingle | QA Mathematics Tripathi, Neeraj Kumar Das, Subir Ong, Seng Huat Jafari, Hossein Al Qurashi, Maysaa’ Mohamed Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method |
| title | Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method |
| title_full | Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method |
| title_fullStr | Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method |
| title_full_unstemmed | Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method |
| title_short | Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method |
| title_sort | solution of time fractional cahn hilliard equation with reaction term using homotopy analysis method |
| topic | QA Mathematics |
| work_keys_str_mv | AT tripathineerajkumar solutionoftimefractionalcahnhilliardequationwithreactiontermusinghomotopyanalysismethod AT dassubir solutionoftimefractionalcahnhilliardequationwithreactiontermusinghomotopyanalysismethod AT ongsenghuat solutionoftimefractionalcahnhilliardequationwithreactiontermusinghomotopyanalysismethod AT jafarihossein solutionoftimefractionalcahnhilliardequationwithreactiontermusinghomotopyanalysismethod AT alqurashimaysaamohamed solutionoftimefractionalcahnhilliardequationwithreactiontermusinghomotopyanalysismethod |