Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials
To solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and Müntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocatio...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/11/2076 |
| _version_ | 1797457614672494592 |
|---|---|
| author | Haifa Bin Jebreen Carlo Cattani |
| author_facet | Haifa Bin Jebreen Carlo Cattani |
| author_sort | Haifa Bin Jebreen |
| collection | DOAJ |
| description | To solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and Müntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocation points in this study are selected to be uniformly spaced meshes or the roots of shifted Legendre and Chebyshev polynomials. Müntz-Legendre polynomials have the interesting property that their fractional derivative is also a Müntz-Legendre polynomial. This property ensures that these bases do not face the problems associated with using the classical orthogonal polynomials when solving fractional equations using the collocation method. The numerical simulations illustrate the method’s effectiveness and accuracy. |
| first_indexed | 2024-03-09T16:24:33Z |
| format | Article |
| id | doaj.art-5cea6f7865cd4e2fb02fe8fe3d7b97a8 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:24:33Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5cea6f7865cd4e2fb02fe8fe3d7b97a82023-11-24T15:09:00ZengMDPI AGSymmetry2073-89942023-11-011511207610.3390/sym15112076Solving Fractional Gas Dynamics Equation Using Müntz–Legendre PolynomialsHaifa Bin Jebreen0Carlo Cattani1Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaEngineering School (DEIM), University of Tuscia, Largo dell’Università, 01100 Viterbo, ItalyTo solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and Müntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocation points in this study are selected to be uniformly spaced meshes or the roots of shifted Legendre and Chebyshev polynomials. Müntz-Legendre polynomials have the interesting property that their fractional derivative is also a Müntz-Legendre polynomial. This property ensures that these bases do not face the problems associated with using the classical orthogonal polynomials when solving fractional equations using the collocation method. The numerical simulations illustrate the method’s effectiveness and accuracy.https://www.mdpi.com/2073-8994/15/11/2076fractional partial differential equationsgas dynamic equationMüntz–Legendre polynomialscollocation method |
| spellingShingle | Haifa Bin Jebreen Carlo Cattani Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials Symmetry fractional partial differential equations gas dynamic equation Müntz–Legendre polynomials collocation method |
| title | Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials |
| title_full | Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials |
| title_fullStr | Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials |
| title_full_unstemmed | Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials |
| title_short | Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials |
| title_sort | solving fractional gas dynamics equation using muntz legendre polynomials |
| topic | fractional partial differential equations gas dynamic equation Müntz–Legendre polynomials collocation method |
| url | https://www.mdpi.com/2073-8994/15/11/2076 |
| work_keys_str_mv | AT haifabinjebreen solvingfractionalgasdynamicsequationusingmuntzlegendrepolynomials AT carlocattani solvingfractionalgasdynamicsequationusingmuntzlegendrepolynomials |