Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations
This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/5768323 |
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| _version_ | 1832552559387082752 |
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| author | Habtamu Garoma Debela Solomon Bati Kejela Ayana Deressa Negassa |
| author_facet | Habtamu Garoma Debela Solomon Bati Kejela Ayana Deressa Negassa |
| author_sort | Habtamu Garoma Debela |
| collection | DOAJ |
| description | This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on four model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method. |
| format | Article |
| id | doaj-art-4422b1900f9d4b8f9dbbf4d21cfd8212 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-4422b1900f9d4b8f9dbbf4d21cfd82122025-02-03T05:58:22ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/57683235768323Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference EquationsHabtamu Garoma Debela0Solomon Bati Kejela1Ayana Deressa Negassa2Department of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaDepartment of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaDepartment of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaThis paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on four model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.http://dx.doi.org/10.1155/2020/5768323 |
| spellingShingle | Habtamu Garoma Debela Solomon Bati Kejela Ayana Deressa Negassa Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations International Journal of Differential Equations |
| title | Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations |
| title_full | Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations |
| title_fullStr | Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations |
| title_full_unstemmed | Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations |
| title_short | Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations |
| title_sort | exponentially fitted numerical method for singularly perturbed differential difference equations |
| url | http://dx.doi.org/10.1155/2020/5768323 |
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