Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation
This paper focuses on an efficient spline-based numerical technique for numerically addressing a second-order Volterra partial integrodifferential equation. The time derivative is discretized using a finite difference scheme, while the space derivative is approximated using the extended cubic B-spli...
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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/10.1155/2022/5431057 |
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| _version_ | 1832554847692390400 |
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| author | Reny George Muhammad Yaseen Sana Khan |
| author_facet | Reny George Muhammad Yaseen Sana Khan |
| author_sort | Reny George |
| collection | DOAJ |
| description | This paper focuses on an efficient spline-based numerical technique for numerically addressing a second-order Volterra partial integrodifferential equation. The time derivative is discretized using a finite difference scheme, while the space derivative is approximated using the extended cubic B-spline basis. The scheme is also tested for stability study to ensure that the errors do not accumulate. The convergence of the proposed scheme is also investigated. The scheme’s key benefit is that the approximate solution is produced as a smooth piecewise continuous function allowing us to approximate the solution at any location in the domain. Numerical study is performed, and the comparison of results is made to previously reported results in the literature to show the efficiency of the suggested scheme. |
| format | Article |
| id | doaj-art-8a8275265fbb4838a14221a3489c41d9 |
| 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-8a8275265fbb4838a14221a3489c41d92025-02-03T05:50:18ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/5431057Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential EquationReny George0Muhammad Yaseen1Sana Khan2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis paper focuses on an efficient spline-based numerical technique for numerically addressing a second-order Volterra partial integrodifferential equation. The time derivative is discretized using a finite difference scheme, while the space derivative is approximated using the extended cubic B-spline basis. The scheme is also tested for stability study to ensure that the errors do not accumulate. The convergence of the proposed scheme is also investigated. The scheme’s key benefit is that the approximate solution is produced as a smooth piecewise continuous function allowing us to approximate the solution at any location in the domain. Numerical study is performed, and the comparison of results is made to previously reported results in the literature to show the efficiency of the suggested scheme.http://dx.doi.org/10.1155/2022/5431057 |
| spellingShingle | Reny George Muhammad Yaseen Sana Khan Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation Journal of Function Spaces |
| title | Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation |
| title_full | Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation |
| title_fullStr | Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation |
| title_full_unstemmed | Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation |
| title_short | Collocation Approach Based on an Extended Cubic B-Spline for a Second-Order Volterra Partial Integrodifferential Equation |
| title_sort | collocation approach based on an extended cubic b spline for a second order volterra partial integrodifferential equation |
| url | http://dx.doi.org/10.1155/2022/5431057 |
| work_keys_str_mv | AT renygeorge collocationapproachbasedonanextendedcubicbsplineforasecondordervolterrapartialintegrodifferentialequation AT muhammadyaseen collocationapproachbasedonanextendedcubicbsplineforasecondordervolterrapartialintegrodifferentialequation AT sanakhan collocationapproachbasedonanextendedcubicbsplineforasecondordervolterrapartialintegrodifferentialequation |