A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations
The present study focuses on designing a multi-step technique, known as the block-by-block technique, to provide the numerical solution for a category of nonlinear fractional two-dimensional Volterra integro-differential equations. The proposed technique is a block-by-block method based on Romberg’s...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-11-01
|
| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000803 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850063830184361984 |
|---|---|
| author | F. Afiatdoust M.H. Heydari M.M. Hosseini M. Mohseni Moghadam |
| author_facet | F. Afiatdoust M.H. Heydari M.M. Hosseini M. Mohseni Moghadam |
| author_sort | F. Afiatdoust |
| collection | DOAJ |
| description | The present study focuses on designing a multi-step technique, known as the block-by-block technique, to provide the numerical solution for a category of nonlinear fractional two-dimensional Volterra integro-differential equations. The proposed technique is a block-by-block method based on Romberg’s numerical integration formula, which simultaneously obtains highly accurate solutions at certain nodes without requiring initial starting values. The convergence analysis of the established method for the aforementioned equations is investigated using Gronwall’s inequality. Several numerical tests are presented to demonstrate the accuracy, speed, and good performance of the procedure. |
| format | Article |
| id | doaj-art-e6c884a5b3884b0488a54581b284416d |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-e6c884a5b3884b0488a54581b284416d2025-08-20T02:49:29ZengElsevierResults in Applied Mathematics2590-03742024-11-012410051010.1016/j.rinam.2024.100510A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equationsF. Afiatdoust0M.H. Heydari1M.M. Hosseini2M. Mohseni Moghadam3Department of applide Mathematics, Faculty of Mathematics and computer, Shahid Bahonar University of Kerman, Kerman, IranDepartment of Mathematics, Shiraz University of Technology, Shiraz, Iran; Corresponding author.Department of applide Mathematics, Faculty of Mathematics and computer, Shahid Bahonar University of Kerman, Kerman, IranDepartment of applide Mathematics, Faculty of Mathematics and computer, Shahid Bahonar University of Kerman, Kerman, IranThe present study focuses on designing a multi-step technique, known as the block-by-block technique, to provide the numerical solution for a category of nonlinear fractional two-dimensional Volterra integro-differential equations. The proposed technique is a block-by-block method based on Romberg’s numerical integration formula, which simultaneously obtains highly accurate solutions at certain nodes without requiring initial starting values. The convergence analysis of the established method for the aforementioned equations is investigated using Gronwall’s inequality. Several numerical tests are presented to demonstrate the accuracy, speed, and good performance of the procedure.http://www.sciencedirect.com/science/article/pii/S2590037424000803Fractional two-dimensional Volterra integral equationsRomberg quadrature formulaBlock-by-block methodConvergence analysis |
| spellingShingle | F. Afiatdoust M.H. Heydari M.M. Hosseini M. Mohseni Moghadam A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations Results in Applied Mathematics Fractional two-dimensional Volterra integral equations Romberg quadrature formula Block-by-block method Convergence analysis |
| title | A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations |
| title_full | A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations |
| title_fullStr | A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations |
| title_full_unstemmed | A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations |
| title_short | A numerical technique for a class of nonlinear fractional 2D Volterra integro-differential equations |
| title_sort | numerical technique for a class of nonlinear fractional 2d volterra integro differential equations |
| topic | Fractional two-dimensional Volterra integral equations Romberg quadrature formula Block-by-block method Convergence analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424000803 |
| work_keys_str_mv | AT fafiatdoust anumericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT mhheydari anumericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT mmhosseini anumericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT mmohsenimoghadam anumericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT fafiatdoust numericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT mhheydari numericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT mmhosseini numericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations AT mmohsenimoghadam numericaltechniqueforaclassofnonlinearfractional2dvolterraintegrodifferentialequations |