A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models
In this paper, a new numerical technique is proposed for the simulations of advection-diffusion-reaction type elliptic and parabolic interface models. The proposed technique comprises of the Haar wavelet collocation method and the finite difference method. In this technique, the spatial derivative i...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/1541486 |
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| author | Gule Rana Muhammad Asif Nadeem Haider Rubi Bilal Muhammad Ahsan Qasem Al-Mdallal Fahd Jarad |
| author_facet | Gule Rana Muhammad Asif Nadeem Haider Rubi Bilal Muhammad Ahsan Qasem Al-Mdallal Fahd Jarad |
| author_sort | Gule Rana |
| collection | DOAJ |
| description | In this paper, a new numerical technique is proposed for the simulations of advection-diffusion-reaction type elliptic and parabolic interface models. The proposed technique comprises of the Haar wavelet collocation method and the finite difference method. In this technique, the spatial derivative is approximated by truncated Haar wavelet series, while for temporal derivative, the finite difference formula is used. The diffusion coefficients, advection coefficients, and reaction coefficients are considered discontinuously across the fixed interface. The newly established numerical technique is applied to both linear and nonlinear benchmark interface models. In the case of linear interface models, Gauss elimination method is used, whereas for nonlinear interface models, the nonlinearity is removed by using the quasi-Newton linearization technique. The L∞ errors are calculated for different number of collocation points. The obtained numerical results are compared with the immersed interface method. The stability and convergence of the method are also discussed. On the whole, the numerical results show more efficiency, better accuracy, and simpler applicability of the newly developed numerical technique compared to the existing methods in literature. |
| format | Article |
| id | doaj-art-299fff80f1e344f8985e7a2378e32330 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-299fff80f1e344f8985e7a2378e323302025-02-03T01:22:52ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/1541486A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface ModelsGule Rana0Muhammad Asif1Nadeem Haider2Rubi Bilal3Muhammad Ahsan4Qasem Al-Mdallal5Fahd Jarad6Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematical SciencesDepartment of MathematicsIn this paper, a new numerical technique is proposed for the simulations of advection-diffusion-reaction type elliptic and parabolic interface models. The proposed technique comprises of the Haar wavelet collocation method and the finite difference method. In this technique, the spatial derivative is approximated by truncated Haar wavelet series, while for temporal derivative, the finite difference formula is used. The diffusion coefficients, advection coefficients, and reaction coefficients are considered discontinuously across the fixed interface. The newly established numerical technique is applied to both linear and nonlinear benchmark interface models. In the case of linear interface models, Gauss elimination method is used, whereas for nonlinear interface models, the nonlinearity is removed by using the quasi-Newton linearization technique. The L∞ errors are calculated for different number of collocation points. The obtained numerical results are compared with the immersed interface method. The stability and convergence of the method are also discussed. On the whole, the numerical results show more efficiency, better accuracy, and simpler applicability of the newly developed numerical technique compared to the existing methods in literature.http://dx.doi.org/10.1155/2022/1541486 |
| spellingShingle | Gule Rana Muhammad Asif Nadeem Haider Rubi Bilal Muhammad Ahsan Qasem Al-Mdallal Fahd Jarad A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models Journal of Function Spaces |
| title | A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models |
| title_full | A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models |
| title_fullStr | A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models |
| title_full_unstemmed | A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models |
| title_short | A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models |
| title_sort | modified algorithm based on haar wavelets for the numerical simulation of interface models |
| url | http://dx.doi.org/10.1155/2022/1541486 |
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