Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method
We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acqui...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/1705651 |
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| author | Mohamed R. Ali Mohamed M. Mousa Wen-Xiu Ma |
| author_facet | Mohamed R. Ali Mohamed M. Mousa Wen-Xiu Ma |
| author_sort | Mohamed R. Ali |
| collection | DOAJ |
| description | We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acquire the HOBW implementation matrix of the integration to derive the procedure of solving these kind integral equations. The explained technique is delineated with two numerical cases to demonstrate the benefit of the technique used by us. At last, the exchange uncovers the way that the strategy utilized here is basic in usage. |
| format | Article |
| id | doaj-art-01e3f60319dc44009ef5b74bb2cc868f |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-01e3f60319dc44009ef5b74bb2cc868f2025-02-03T06:00:14ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/17056511705651Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW MethodMohamed R. Ali0Mohamed M. Mousa1Wen-Xiu Ma2Department of Mathematics, Benha Faculty of Engineering, Benha University, Benha, EgyptDepartment of Mathematics, Benha Faculty of Engineering, Benha University, Benha, EgyptDepartment of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USAWe present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acquire the HOBW implementation matrix of the integration to derive the procedure of solving these kind integral equations. The explained technique is delineated with two numerical cases to demonstrate the benefit of the technique used by us. At last, the exchange uncovers the way that the strategy utilized here is basic in usage.http://dx.doi.org/10.1155/2019/1705651 |
| spellingShingle | Mohamed R. Ali Mohamed M. Mousa Wen-Xiu Ma Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method Advances in Mathematical Physics |
| title | Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method |
| title_full | Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method |
| title_fullStr | Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method |
| title_full_unstemmed | Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method |
| title_short | Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method |
| title_sort | solution of nonlinear volterra integral equations with weakly singular kernel by using the hobw method |
| url | http://dx.doi.org/10.1155/2019/1705651 |
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