Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions
This article aims to present a new approach based on the operational matrix method for solving integro-differential equations using numerical techniques. In this method, we employ fourth-degree hat functions (FDHFs) to construct operational matrices. The approach involves two main steps. First, we u...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000426 |
| _version_ | 1797390380081086464 |
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| author | Jehad K. Mohammed Ayad R. Khudair |
| author_facet | Jehad K. Mohammed Ayad R. Khudair |
| author_sort | Jehad K. Mohammed |
| collection | DOAJ |
| description | This article aims to present a new approach based on the operational matrix method for solving integro-differential equations using numerical techniques. In this method, we employ fourth-degree hat functions (FDHFs) to construct operational matrices. The approach involves two main steps. First, we utilize FDHFs to create operational matrices, which allows us to transform the given problem into a system of algebraic equations. The second step involves solving these algebraic equations numerically. Additionally, we provide an analysis of the errors involved and compare the proposed method with existing techniques. The results demonstrate that the proposed method outperforms its counterparts, highlighting its superiority. |
| first_indexed | 2024-03-08T23:10:53Z |
| format | Article |
| id | doaj.art-dba2be22ab9845be9889f3f1d6a48852 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:53Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-dba2be22ab9845be9889f3f1d6a488522023-12-15T07:26:41ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100529Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functionsJehad K. Mohammed0Ayad R. Khudair1Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, Iraq; Department of Materials Management Techniques, Amara Technical Institute, Southern Technical University, IraqDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq; Corresponding author.This article aims to present a new approach based on the operational matrix method for solving integro-differential equations using numerical techniques. In this method, we employ fourth-degree hat functions (FDHFs) to construct operational matrices. The approach involves two main steps. First, we utilize FDHFs to create operational matrices, which allows us to transform the given problem into a system of algebraic equations. The second step involves solving these algebraic equations numerically. Additionally, we provide an analysis of the errors involved and compare the proposed method with existing techniques. The results demonstrate that the proposed method outperforms its counterparts, highlighting its superiority.http://www.sciencedirect.com/science/article/pii/S2666818123000426Fourth-degree hat functionsNonlinear Volterra integro-differential equationsOperational matrixError analysis |
| spellingShingle | Jehad K. Mohammed Ayad R. Khudair Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions Partial Differential Equations in Applied Mathematics Fourth-degree hat functions Nonlinear Volterra integro-differential equations Operational matrix Error analysis |
| title | Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions |
| title_full | Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions |
| title_fullStr | Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions |
| title_full_unstemmed | Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions |
| title_short | Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions |
| title_sort | integro differential equations numerical solution by a new operational matrix based on fourth order hat functions |
| topic | Fourth-degree hat functions Nonlinear Volterra integro-differential equations Operational matrix Error analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000426 |
| work_keys_str_mv | AT jehadkmohammed integrodifferentialequationsnumericalsolutionbyanewoperationalmatrixbasedonfourthorderhatfunctions AT ayadrkhudair integrodifferentialequationsnumericalsolutionbyanewoperationalmatrixbasedonfourthorderhatfunctions |