Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
The nonlinear integral equations are usually difficult to solve analytically and in many cases, it is required to obtain the approximate solutions. The nonlinear Volterra integral equation of second kind is one of them. This dissertation compares two methods that are used in order to solve nonlinear...
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| Format: | Thesis |
| Language: | English |
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2014
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| Online Access: | http://eprints.utm.my/51411/25/SitiAminahMohamadMFS2014.pdf |
| _version_ | 1796859637503361024 |
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| author | Mohamad Sapawi, Siti Aminah |
| author_facet | Mohamad Sapawi, Siti Aminah |
| author_sort | Mohamad Sapawi, Siti Aminah |
| collection | ePrints |
| description | The nonlinear integral equations are usually difficult to solve analytically and in many cases, it is required to obtain the approximate solutions. The nonlinear Volterra integral equation of second kind is one of them. This dissertation compares two methods that are used in order to solve nonlinear Volterra integral equation of second kind. Those are Chebyshev polynomials and Adomian decomposition method. The Chebyshev polynomials are developed to approximate the solution of linear and nonlinear Volterra integral equations. While, Adomian decomposition method, is a method that can be applied directly for all type of linear and nonlinear integral equations and maintain high accuracy of numerical solution. Hence, the best method is picked based on the absolute error that will be compared with the exact solution. |
| first_indexed | 2024-03-05T19:30:07Z |
| format | Thesis |
| id | utm.eprints-51411 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T19:30:07Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | utm.eprints-514112020-07-13T03:53:41Z http://eprints.utm.my/51411/ Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind Mohamad Sapawi, Siti Aminah QA Mathematics The nonlinear integral equations are usually difficult to solve analytically and in many cases, it is required to obtain the approximate solutions. The nonlinear Volterra integral equation of second kind is one of them. This dissertation compares two methods that are used in order to solve nonlinear Volterra integral equation of second kind. Those are Chebyshev polynomials and Adomian decomposition method. The Chebyshev polynomials are developed to approximate the solution of linear and nonlinear Volterra integral equations. While, Adomian decomposition method, is a method that can be applied directly for all type of linear and nonlinear integral equations and maintain high accuracy of numerical solution. Hence, the best method is picked based on the absolute error that will be compared with the exact solution. 2014-06 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/51411/25/SitiAminahMohamadMFS2014.pdf Mohamad Sapawi, Siti Aminah (2014) Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86516 |
| spellingShingle | QA Mathematics Mohamad Sapawi, Siti Aminah Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| title | Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| title_full | Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| title_fullStr | Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| title_full_unstemmed | Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| title_short | Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| title_sort | comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind |
| topic | QA Mathematics |
| url | http://eprints.utm.my/51411/25/SitiAminahMohamadMFS2014.pdf |
| work_keys_str_mv | AT mohamadsapawisitiaminah comparingchebyshevpolynomialsandadomiandecompositionmethodinsolvingnonlinearvolterraintegralequationsofsecondkind |