Numerical investigation of singularly perturbed time lag parabolic differential-difference equations
This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the θ method (θ=1) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besi...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024172465 |
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| author | Imiru Takele Daba Wondwosen Gebeyaw Melesse Fasika Wondimu Gelu Guta Demisu Kebede |
| author_facet | Imiru Takele Daba Wondwosen Gebeyaw Melesse Fasika Wondimu Gelu Guta Demisu Kebede |
| author_sort | Imiru Takele Daba |
| collection | DOAJ |
| description | This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the θ method (θ=1) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme. The applicability of the proposed approach is confirmed through some numerical examples. Furthermore, we have improved the convergence from almost first to almost second order. |
| format | Article |
| id | doaj-art-1ecd5acef5f1476bb0c511215a3e563a |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-1ecd5acef5f1476bb0c511215a3e563a2025-01-17T04:50:32ZengElsevierHeliyon2405-84402025-01-01111e41215Numerical investigation of singularly perturbed time lag parabolic differential-difference equationsImiru Takele Daba0Wondwosen Gebeyaw Melesse1Fasika Wondimu Gelu2Guta Demisu Kebede3Department of Mathematics, Salale University, Fitche, Ethiopia; Corresponding author.Department of Mathematics, Dilla University, Dilla, EthiopiaDepartment of Mathematics, Dilla University, Dilla, EthiopiaDepartment of Mathematics, Dilla University, Dilla, EthiopiaThis paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the θ method (θ=1) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme. The applicability of the proposed approach is confirmed through some numerical examples. Furthermore, we have improved the convergence from almost first to almost second order.http://www.sciencedirect.com/science/article/pii/S2405844024172465Differential- difference equationθ-methodTime lagNon-standard finite difference methodUniformly convergent scheme |
| spellingShingle | Imiru Takele Daba Wondwosen Gebeyaw Melesse Fasika Wondimu Gelu Guta Demisu Kebede Numerical investigation of singularly perturbed time lag parabolic differential-difference equations Heliyon Differential- difference equation θ-method Time lag Non-standard finite difference method Uniformly convergent scheme |
| title | Numerical investigation of singularly perturbed time lag parabolic differential-difference equations |
| title_full | Numerical investigation of singularly perturbed time lag parabolic differential-difference equations |
| title_fullStr | Numerical investigation of singularly perturbed time lag parabolic differential-difference equations |
| title_full_unstemmed | Numerical investigation of singularly perturbed time lag parabolic differential-difference equations |
| title_short | Numerical investigation of singularly perturbed time lag parabolic differential-difference equations |
| title_sort | numerical investigation of singularly perturbed time lag parabolic differential difference equations |
| topic | Differential- difference equation θ-method Time lag Non-standard finite difference method Uniformly convergent scheme |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024172465 |
| work_keys_str_mv | AT imirutakeledaba numericalinvestigationofsingularlyperturbedtimelagparabolicdifferentialdifferenceequations AT wondwosengebeyawmelesse numericalinvestigationofsingularlyperturbedtimelagparabolicdifferentialdifferenceequations AT fasikawondimugelu numericalinvestigationofsingularlyperturbedtimelagparabolicdifferentialdifferenceequations AT gutademisukebede numericalinvestigationofsingularlyperturbedtimelagparabolicdifferentialdifferenceequations |