Barycentric Lagrange interpolation method for solving Love’s integral equations
Abstract In this paper, we present a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagrange interpolation....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01758-7 |
| _version_ | 1827899818107731968 |
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| author | E. S. Shoukralla B. M. Ahmed |
| author_facet | E. S. Shoukralla B. M. Ahmed |
| author_sort | E. S. Shoukralla |
| collection | DOAJ |
| description | Abstract In this paper, we present a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagrange interpolation. The unknown function is expressed through the product of four matrices. The kernel is interpolated twice, so we get it in the product of five matrices. Additionally, we derive an equivalent linear algebraic system to the solution by substituting the matrix-vector barycentric interpolated unknown function together with the double interpolated kernel into both sides of the integral equation. Thus, there was no need to employ the collocation method. The obtained results converge strongly with the approximate analytical solutions, in addition to being uniformly approximated, continuous, and even, which proves the validity of the solution by the presented method. |
| first_indexed | 2024-03-12T23:22:47Z |
| format | Article |
| id | doaj.art-e88b5a6a8f4a48b4be3bd3c17ec23ffd |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-12T23:22:47Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-e88b5a6a8f4a48b4be3bd3c17ec23ffd2023-07-16T11:23:14ZengSpringerOpenBoundary Value Problems1687-27702023-07-01202311710.1186/s13661-023-01758-7Barycentric Lagrange interpolation method for solving Love’s integral equationsE. S. Shoukralla0B. M. Ahmed1Dept. of Eng. Math. And Phys., Faculty of Electronic Eng., Menoufia UniversityDept. of Eng. Math. And Phys., Faculty of Engineering and Technology, Future University in EgyptAbstract In this paper, we present a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagrange interpolation. The unknown function is expressed through the product of four matrices. The kernel is interpolated twice, so we get it in the product of five matrices. Additionally, we derive an equivalent linear algebraic system to the solution by substituting the matrix-vector barycentric interpolated unknown function together with the double interpolated kernel into both sides of the integral equation. Thus, there was no need to employ the collocation method. The obtained results converge strongly with the approximate analytical solutions, in addition to being uniformly approximated, continuous, and even, which proves the validity of the solution by the presented method.https://doi.org/10.1186/s13661-023-01758-7ElectrostaticsPolymer structuresAerodynamicsFracture mechanics hydrodynamicsElasticity |
| spellingShingle | E. S. Shoukralla B. M. Ahmed Barycentric Lagrange interpolation method for solving Love’s integral equations Boundary Value Problems Electrostatics Polymer structures Aerodynamics Fracture mechanics hydrodynamics Elasticity |
| title | Barycentric Lagrange interpolation method for solving Love’s integral equations |
| title_full | Barycentric Lagrange interpolation method for solving Love’s integral equations |
| title_fullStr | Barycentric Lagrange interpolation method for solving Love’s integral equations |
| title_full_unstemmed | Barycentric Lagrange interpolation method for solving Love’s integral equations |
| title_short | Barycentric Lagrange interpolation method for solving Love’s integral equations |
| title_sort | barycentric lagrange interpolation method for solving love s integral equations |
| topic | Electrostatics Polymer structures Aerodynamics Fracture mechanics hydrodynamics Elasticity |
| url | https://doi.org/10.1186/s13661-023-01758-7 |
| work_keys_str_mv | AT esshoukralla barycentriclagrangeinterpolationmethodforsolvinglovesintegralequations AT bmahmed barycentriclagrangeinterpolationmethodforsolvinglovesintegralequations |