A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations
In this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations for the two types (3D-MVFIEK2). This method transforms the 3D-MVFIEK2 into a system of linear algebraic equations. The error evaluation fo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/2/196 |
| _version_ | 1797620907278073856 |
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| author | Amr M. S. Mahdy Abbas S. Nagdy Khaled M. Hashem Doaa Sh. Mohamed |
| author_facet | Amr M. S. Mahdy Abbas S. Nagdy Khaled M. Hashem Doaa Sh. Mohamed |
| author_sort | Amr M. S. Mahdy |
| collection | DOAJ |
| description | In this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations for the two types (3D-MVFIEK2). This method transforms the 3D-MVFIEK2 into a system of linear algebraic equations. The error evaluation for the suggested scheme is discussed. This technique is implemented in four examples to illustrate the efficiency and fulfillment of the approach. Examples of numerical solutions to both linear and nonlinear integral equations were used. The Lucas polynomial method and other approaches were contrasted. A collection of tables and figures is used to present the numerical results. We observe that the exact solution differs from the numerical solution if the exact solution is an exponential or trigonometric function, while the numerical solution is the same when the exact solution is a polynomial. The Maple 18 program produced all of the results. |
| first_indexed | 2024-03-11T08:48:14Z |
| format | Article |
| id | doaj.art-c0607406ed084f2c8af4480248207533 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:48:14Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-c0607406ed084f2c8af44802482075332023-11-16T20:37:19ZengMDPI AGFractal and Fractional2504-31102023-02-017219610.3390/fractalfract7020196A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral EquationsAmr M. S. Mahdy0Abbas S. Nagdy1Khaled M. Hashem2Doaa Sh. Mohamed3Department of Mathematics, Faculty of Science, Zagazig University, Zagazig P.O. Box 44519, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig P.O. Box 44519, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig P.O. Box 44519, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig P.O. Box 44519, EgyptIn this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations for the two types (3D-MVFIEK2). This method transforms the 3D-MVFIEK2 into a system of linear algebraic equations. The error evaluation for the suggested scheme is discussed. This technique is implemented in four examples to illustrate the efficiency and fulfillment of the approach. Examples of numerical solutions to both linear and nonlinear integral equations were used. The Lucas polynomial method and other approaches were contrasted. A collection of tables and figures is used to present the numerical results. We observe that the exact solution differs from the numerical solution if the exact solution is an exponential or trigonometric function, while the numerical solution is the same when the exact solution is a polynomial. The Maple 18 program produced all of the results.https://www.mdpi.com/2504-3110/7/2/196three-dimensional Volterra–Fredholm integral equationsLucas polynomialscollocation pointserror estimation |
| spellingShingle | Amr M. S. Mahdy Abbas S. Nagdy Khaled M. Hashem Doaa Sh. Mohamed A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations Fractal and Fractional three-dimensional Volterra–Fredholm integral equations Lucas polynomials collocation points error estimation |
| title | A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations |
| title_full | A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations |
| title_fullStr | A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations |
| title_full_unstemmed | A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations |
| title_short | A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations |
| title_sort | computational technique for solving three dimensional mixed volterra fredholm integral equations |
| topic | three-dimensional Volterra–Fredholm integral equations Lucas polynomials collocation points error estimation |
| url | https://www.mdpi.com/2504-3110/7/2/196 |
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