Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term
A singularly perturbed delay parabolic problem of convection-diffusion type with a discontinuous convection coefficient and source term is examined. In the problem, strong interior layers and weak boundary layers are exhibited due to a large delay in the spatial variable and discontinuity of convect...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1874741 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849413394835177472 |
|---|---|
| author | Mulunesh Amsalu Ayele Awoke Andargie Tiruneh Getachew Adamu Derese |
| author_facet | Mulunesh Amsalu Ayele Awoke Andargie Tiruneh Getachew Adamu Derese |
| author_sort | Mulunesh Amsalu Ayele |
| collection | DOAJ |
| description | A singularly perturbed delay parabolic problem of convection-diffusion type with a discontinuous convection coefficient and source term is examined. In the problem, strong interior layers and weak boundary layers are exhibited due to a large delay in the spatial variable and discontinuity of convection coefficient and source. The problem is discretized by a nonstandard finite difference scheme in the spatial variable and for the time derivative, we used the Crank–Nicolson scheme. To enhance the order of convergence of the spatial variable, the Richardson extrapolation technique is applied. The error analysis of the proposed scheme was carried out and proved that the scheme is uniformly convergent of second order in both spatial and temporal variables. Numerical experiments are performed to verify the theoretical estimates. |
| format | Article |
| id | doaj-art-69dff4cf8cd744dcb6dae093fd67c308 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-69dff4cf8cd744dcb6dae093fd67c3082025-08-20T03:34:08ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1874741Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source TermMulunesh Amsalu Ayele0Awoke Andargie Tiruneh1Getachew Adamu Derese2Department of MathematicsDepartment of MathematicsDepartment of MathematicsA singularly perturbed delay parabolic problem of convection-diffusion type with a discontinuous convection coefficient and source term is examined. In the problem, strong interior layers and weak boundary layers are exhibited due to a large delay in the spatial variable and discontinuity of convection coefficient and source. The problem is discretized by a nonstandard finite difference scheme in the spatial variable and for the time derivative, we used the Crank–Nicolson scheme. To enhance the order of convergence of the spatial variable, the Richardson extrapolation technique is applied. The error analysis of the proposed scheme was carried out and proved that the scheme is uniformly convergent of second order in both spatial and temporal variables. Numerical experiments are performed to verify the theoretical estimates.http://dx.doi.org/10.1155/2022/1874741 |
| spellingShingle | Mulunesh Amsalu Ayele Awoke Andargie Tiruneh Getachew Adamu Derese Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term Journal of Mathematics |
| title | Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term |
| title_full | Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term |
| title_fullStr | Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term |
| title_full_unstemmed | Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term |
| title_short | Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term |
| title_sort | uniformly convergent scheme for singularly perturbed space delay parabolic differential equation with discontinuous convection coefficient and source term |
| url | http://dx.doi.org/10.1155/2022/1874741 |
| work_keys_str_mv | AT muluneshamsaluayele uniformlyconvergentschemeforsingularlyperturbedspacedelayparabolicdifferentialequationwithdiscontinuousconvectioncoefficientandsourceterm AT awokeandargietiruneh uniformlyconvergentschemeforsingularlyperturbedspacedelayparabolicdifferentialequationwithdiscontinuousconvectioncoefficientandsourceterm AT getachewadamuderese uniformlyconvergentschemeforsingularlyperturbedspacedelayparabolicdifferentialequationwithdiscontinuousconvectioncoefficientandsourceterm |