Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods
The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial...
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Hindawi Publishing
2014
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| Online Access: | http://www.hindawi.com/journals/jam/2014/654978/cta/ https://library.oum.edu.my/repository/935/ |
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| author | Norhasimah Mahiddin, Siti Aishah Hashim Ali, |
| author_facet | Norhasimah Mahiddin, Siti Aishah Hashim Ali, |
| author_sort | Norhasimah Mahiddin, |
| building | OUM Library |
| collection | Institutional Repository |
| content_provider | Open University Malaysia |
| content_source | OUM Knowledge Repository |
| continent | Asia |
| country | Malaysia |
| description | The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems. (Abstract by authors) |
| format | Article |
| id | my.oum.935 |
| institution | Open University Malaysia |
| publishDate | 2014 |
| publisher | Hindawi Publishing |
| record_format | eprints |
| spelling | my.oum.9352014-03-21T08:46:14Z Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods Norhasimah Mahiddin, Siti Aishah Hashim Ali, QA Mathematics The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems. (Abstract by authors) Hindawi Publishing 2014 Article PeerReviewed http://www.hindawi.com/journals/jam/2014/654978/cta/ Norhasimah Mahiddin, and Siti Aishah Hashim Ali, (2014) Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods. Journal of Applied Mathematics, 14. https://library.oum.edu.my/repository/935/ |
| spellingShingle | QA Mathematics Norhasimah Mahiddin, Siti Aishah Hashim Ali, Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods |
| title | Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods |
| title_full | Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods |
| title_fullStr | Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods |
| title_full_unstemmed | Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods |
| title_short | Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods |
| title_sort | approximate analytical solutions for mathematical model of tumour invasion and metastasis using modified adomian decomposition and homotopy perturbation methods |
| topic | QA Mathematics |
| url | http://www.hindawi.com/journals/jam/2014/654978/cta/ https://library.oum.edu.my/repository/935/ |
| url_provider | http://library.oum.edu.my/repository/ |