Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations
In this paper, the functional Volterra integral equations of the Hammerstein type are studied. First, some conditions that ensure the existence and uniqueness of the solutions to these equations within the space of square-integrable functions are established and then the Euler operational matrix of...
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University of Maragheh
2025-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_719397_0f8d47c010a041c7952add234a1a8a4c.pdf |
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| author | Sohrab Bazm Fatemeh Pahlevani |
| author_facet | Sohrab Bazm Fatemeh Pahlevani |
| author_sort | Sohrab Bazm |
| collection | DOAJ |
| description | In this paper, the functional Volterra integral equations of the Hammerstein type are studied. First, some conditions that ensure the existence and uniqueness of the solutions to these equations within the space of square-integrable functions are established and then the Euler operational matrix of integration is constructed and applied within the collocation method for approximating the solutions. This approach transforms the integral equation into a set of nonlinear algebraic equations, which can be efficiently solved by employing standard numerical methods like Newton's method or Picard iteration. One significant advantage of this method lies in its ability to avoid the need for direct integration to discretize the integral operator. Error estimates are provided and two illustrative examples are included to demonstrate the method’s effectiveness and practical applicability. |
| format | Article |
| id | doaj-art-313ea0b3452244aeb278e4dc03a3658c |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-313ea0b3452244aeb278e4dc03a3658c2025-02-11T05:28:01ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002025-01-0122123325810.22130/scma.2024.2044355.1937719397Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral EquationsSohrab Bazm0Fatemeh Pahlevani1Department of Mathematics, Faculty of Science, University of Maragheh, 55136-553 Maragheh, Iran.Department of Mathematics, Faculty of Science, University of Maragheh, 55136-553 Maragheh, Iran.In this paper, the functional Volterra integral equations of the Hammerstein type are studied. First, some conditions that ensure the existence and uniqueness of the solutions to these equations within the space of square-integrable functions are established and then the Euler operational matrix of integration is constructed and applied within the collocation method for approximating the solutions. This approach transforms the integral equation into a set of nonlinear algebraic equations, which can be efficiently solved by employing standard numerical methods like Newton's method or Picard iteration. One significant advantage of this method lies in its ability to avoid the need for direct integration to discretize the integral operator. Error estimates are provided and two illustrative examples are included to demonstrate the method’s effectiveness and practical applicability.https://scma.maragheh.ac.ir/article_719397_0f8d47c010a041c7952add234a1a8a4c.pdffunctional integral equationshammerstein integral equationscollocation methodeuler polynomialsoperational matrix |
| spellingShingle | Sohrab Bazm Fatemeh Pahlevani Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations Sahand Communications in Mathematical Analysis functional integral equations hammerstein integral equations collocation method euler polynomials operational matrix |
| title | Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations |
| title_full | Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations |
| title_fullStr | Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations |
| title_full_unstemmed | Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations |
| title_short | Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations |
| title_sort | euler operational matrix of integration and collocation method for solving functional integral equations |
| topic | functional integral equations hammerstein integral equations collocation method euler polynomials operational matrix |
| url | https://scma.maragheh.ac.ir/article_719397_0f8d47c010a041c7952add234a1a8a4c.pdf |
| work_keys_str_mv | AT sohrabbazm euleroperationalmatrixofintegrationandcollocationmethodforsolvingfunctionalintegralequations AT fatemehpahlevani euleroperationalmatrixofintegrationandcollocationmethodforsolvingfunctionalintegralequations |