Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem
In this paper, we present a well-organized method to estimate the one-dimensional fractional Rayleigh–Stokes model using the construction of orthogonal Gegenbauer polynomials (GBPs) and Lagrange square interpolation to estimate the time derivative. Therefore, we design an authentic and fast numerica...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2023-08-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0156586 |
| _version_ | 1827821720263720960 |
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| author | H. Mesgarani Y. Esmaeelzade Aghdam M. Khoshkhahtinat B. Farnam |
| author_facet | H. Mesgarani Y. Esmaeelzade Aghdam M. Khoshkhahtinat B. Farnam |
| author_sort | H. Mesgarani |
| collection | DOAJ |
| description | In this paper, we present a well-organized method to estimate the one-dimensional fractional Rayleigh–Stokes model using the construction of orthogonal Gegenbauer polynomials (GBPs) and Lagrange square interpolation to estimate the time derivative. Therefore, we design an authentic and fast numerical calculation approach based on the elaborated convergence rate recovery method. The matrix of the derivative operation of an orthogonal GBP is gained by employing the characteristic of this type of polynomial. The privilege of the numerical method is the orthogonality of the GBP and operational matrices, which reduces time computation and increases speed. Eventually, we propose three numerical examples to check the validity and numerical studies to illustrate the precision and efficiency of the new approach. |
| first_indexed | 2024-03-12T01:49:02Z |
| format | Article |
| id | doaj.art-25f2203974d44ca0a406156cccf5fe39 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-03-12T01:49:02Z |
| publishDate | 2023-08-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-25f2203974d44ca0a406156cccf5fe392023-09-08T16:03:29ZengAIP Publishing LLCAIP Advances2158-32262023-08-01138085024085024-910.1063/5.0156586Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problemH. Mesgarani0Y. Esmaeelzade Aghdam1M. Khoshkhahtinat2B. Farnam3Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785 -136, I. R. IranDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785 -136, I. R. IranDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785 -136, I. R. IranDepartment of Mathematics, Faculty of Science, Qom University of Technology, Qom, I. R. IranIn this paper, we present a well-organized method to estimate the one-dimensional fractional Rayleigh–Stokes model using the construction of orthogonal Gegenbauer polynomials (GBPs) and Lagrange square interpolation to estimate the time derivative. Therefore, we design an authentic and fast numerical calculation approach based on the elaborated convergence rate recovery method. The matrix of the derivative operation of an orthogonal GBP is gained by employing the characteristic of this type of polynomial. The privilege of the numerical method is the orthogonality of the GBP and operational matrices, which reduces time computation and increases speed. Eventually, we propose three numerical examples to check the validity and numerical studies to illustrate the precision and efficiency of the new approach.http://dx.doi.org/10.1063/5.0156586 |
| spellingShingle | H. Mesgarani Y. Esmaeelzade Aghdam M. Khoshkhahtinat B. Farnam Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem AIP Advances |
| title | Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem |
| title_full | Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem |
| title_fullStr | Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem |
| title_full_unstemmed | Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem |
| title_short | Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem |
| title_sort | analysis of the numerical scheme of the one dimensional fractional rayleigh stokes model arising in a heated generalized problem |
| url | http://dx.doi.org/10.1063/5.0156586 |
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