Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method
In this paper, we consider mostly the inhomogeneous Fitzhugh-Nagumo-Huxley equation with its initial value. Adomian Decomposition Method (ADM), Modified Decomposition Method (MDM) and Laplace Decomposition Method (LDM) are applied to this equation to obtain the solution that satisfies the given init...
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Kyrgyz Turkish Manas University
2017-05-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/575988 |
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| author | Ömer Faruh Gözükızıl Hami Gündoğdu |
| author_facet | Ömer Faruh Gözükızıl Hami Gündoğdu |
| author_sort | Ömer Faruh Gözükızıl |
| collection | DOAJ |
| description | In this paper, we consider mostly the inhomogeneous Fitzhugh-Nagumo-Huxley equation with its initial value. Adomian Decomposition Method (ADM), Modified Decomposition Method (MDM) and Laplace Decomposition Method (LDM) are applied to this equation to obtain the solution that satisfies the given initial condition. It can be easily seen that each method gives the exactly same solution. And then, the inhomogeneous Boussinesq equation and another nonlinear partial differential equation subject to given initial values are solved by using LDM. In applications of the methods, it is demonstrated that we get the solution with a fast convergence by using the advantage of the noise terms. Moreover, we do not need to turn the nonlinear terms into linear ones since Adomian polynomials are used. Therefore, it is deduced that these methods are, indeed, effective and suitable for the nonlinear partial differential equations with the initial values. |
| format | Article |
| id | doaj-art-b3b3672d4aa04e42bffb5903c7ec60df |
| institution | Kabale University |
| issn | 1694-7398 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-b3b3672d4aa04e42bffb5903c7ec60df2025-02-03T12:02:37ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982017-05-01511131437Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition MethodÖmer Faruh Gözükızıl0Hami Gündoğdu1Department of Mathematics, Sakarya University, Sakarya, TurkeyDepartment of Mathematics, Sakarya University, Sakarya, TurkeyIn this paper, we consider mostly the inhomogeneous Fitzhugh-Nagumo-Huxley equation with its initial value. Adomian Decomposition Method (ADM), Modified Decomposition Method (MDM) and Laplace Decomposition Method (LDM) are applied to this equation to obtain the solution that satisfies the given initial condition. It can be easily seen that each method gives the exactly same solution. And then, the inhomogeneous Boussinesq equation and another nonlinear partial differential equation subject to given initial values are solved by using LDM. In applications of the methods, it is demonstrated that we get the solution with a fast convergence by using the advantage of the noise terms. Moreover, we do not need to turn the nonlinear terms into linear ones since Adomian polynomials are used. Therefore, it is deduced that these methods are, indeed, effective and suitable for the nonlinear partial differential equations with the initial values.https://dergipark.org.tr/en/download/article-file/575988laplace decomposition methodadomian decomposition methodmodified decomposition methodfitzhugh- nagumo-huxley equation and the noise termsadomian ayrışma metodudeğiştirilmiş ayrışma metodulaplace ayrışma metodufitzhughnagumo-huxley denklemi and parazit terimler |
| spellingShingle | Ömer Faruh Gözükızıl Hami Gündoğdu Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method MANAS: Journal of Engineering laplace decomposition method adomian decomposition method modified decomposition method fitzhugh- nagumo-huxley equation and the noise terms adomian ayrışma metodu değiştirilmiş ayrışma metodu laplace ayrışma metodu fitzhughnagumo-huxley denklemi and parazit terimler |
| title | Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method |
| title_full | Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method |
| title_fullStr | Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method |
| title_full_unstemmed | Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method |
| title_short | Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method |
| title_sort | solving nonlinear partial differential equations by using adomian decomposition method modified decomposition method and laplace decomposition method |
| topic | laplace decomposition method adomian decomposition method modified decomposition method fitzhugh- nagumo-huxley equation and the noise terms adomian ayrışma metodu değiştirilmiş ayrışma metodu laplace ayrışma metodu fitzhughnagumo-huxley denklemi and parazit terimler |
| url | https://dergipark.org.tr/en/download/article-file/575988 |
| work_keys_str_mv | AT omerfaruhgozukızıl solvingnonlinearpartialdifferentialequationsbyusingadomiandecompositionmethodmodifieddecompositionmethodandlaplacedecompositionmethod AT hamigundogdu solvingnonlinearpartialdifferentialequationsbyusingadomiandecompositionmethodmodifieddecompositionmethodandlaplacedecompositionmethod |