Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme
This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/1661661 |
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| _version_ | 1832548978098438144 |
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| author | Dagnachew Mengstie Tefera Awoke Andargie Tiruneh Getachew Adamu Derese |
| author_facet | Dagnachew Mengstie Tefera Awoke Andargie Tiruneh Getachew Adamu Derese |
| author_sort | Dagnachew Mengstie Tefera |
| collection | DOAJ |
| description | This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained Oh2+k2 uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature. |
| format | Article |
| id | doaj-art-d8d9727e0ce54ddc8f1adc8495f2085f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d8d9727e0ce54ddc8f1adc8495f2085f2025-02-03T06:12:31ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/16616611661661Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator SchemeDagnachew Mengstie Tefera0Awoke Andargie Tiruneh1Getachew Adamu Derese2Department of Mathematics, Bahir Dar University, EthiopiaDepartment of Mathematics, Bahir Dar University, EthiopiaDepartment of Mathematics, Bahir Dar University, EthiopiaThis paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained Oh2+k2 uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature.http://dx.doi.org/10.1155/2021/1661661 |
| spellingShingle | Dagnachew Mengstie Tefera Awoke Andargie Tiruneh Getachew Adamu Derese Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme Abstract and Applied Analysis |
| title | Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme |
| title_full | Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme |
| title_fullStr | Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme |
| title_full_unstemmed | Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme |
| title_short | Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme |
| title_sort | numerical treatment on parabolic singularly perturbed differential difference equation via fitted operator scheme |
| url | http://dx.doi.org/10.1155/2021/1661661 |
| work_keys_str_mv | AT dagnachewmengstietefera numericaltreatmentonparabolicsingularlyperturbeddifferentialdifferenceequationviafittedoperatorscheme AT awokeandargietiruneh numericaltreatmentonparabolicsingularlyperturbeddifferentialdifferenceequationviafittedoperatorscheme AT getachewadamuderese numericaltreatmentonparabolicsingularlyperturbeddifferentialdifferenceequationviafittedoperatorscheme |