Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials
The goal of this paper is study the mixed integral equation with singular kernel in two-dimensional adding to the time in the Volterra integral term numerically. We established the problem from the plane strain problem for the bounded layer medium composed of different materials that contains a crac...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/3398175 |
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| author | A. M. Al-Bugami |
| author_facet | A. M. Al-Bugami |
| author_sort | A. M. Al-Bugami |
| collection | DOAJ |
| description | The goal of this paper is study the mixed integral equation with singular kernel in two-dimensional adding to the time in the Volterra integral term numerically. We established the problem from the plane strain problem for the bounded layer medium composed of different materials that contains a crack on one of the interface. Also, the existence of a unique solution of the equation proved. Therefore, a numerical method is used to translate our problem to a system of two-dimensional Fredholm integral equations (STDFIEs). Then, Toeplitz matrix (TMM) and the Nystrom product methods (NPM) are used to solve the STDFIEs with Cauchy kernel. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the methods. The codes were written in Maple. |
| format | Article |
| id | doaj-art-6cee47b7af2f4b6f8e65fb74d9e156ae |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-6cee47b7af2f4b6f8e65fb74d9e156ae2025-08-20T03:34:10ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/3398175Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of MaterialsA. M. Al-Bugami0Department of Mathematics and StatisticsThe goal of this paper is study the mixed integral equation with singular kernel in two-dimensional adding to the time in the Volterra integral term numerically. We established the problem from the plane strain problem for the bounded layer medium composed of different materials that contains a crack on one of the interface. Also, the existence of a unique solution of the equation proved. Therefore, a numerical method is used to translate our problem to a system of two-dimensional Fredholm integral equations (STDFIEs). Then, Toeplitz matrix (TMM) and the Nystrom product methods (NPM) are used to solve the STDFIEs with Cauchy kernel. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the methods. The codes were written in Maple.http://dx.doi.org/10.1155/2022/3398175 |
| spellingShingle | A. M. Al-Bugami Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials Advances in Mathematical Physics |
| title | Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials |
| title_full | Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials |
| title_fullStr | Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials |
| title_full_unstemmed | Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials |
| title_short | Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials |
| title_sort | numerical treating of mixed integral equation two dimensional in surface cracks in finite layers of materials |
| url | http://dx.doi.org/10.1155/2022/3398175 |
| work_keys_str_mv | AT amalbugami numericaltreatingofmixedintegralequationtwodimensionalinsurfacecracksinfinitelayersofmaterials |