Matrix Form of Deriving High Order Schemes for the First Derivative
For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a speci...
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| Format: | Article |
| Language: | English |
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University of Baghdad, College of Science for Women
2020-09-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4329 |
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| author | Hassan Abd Salman Al-Dujaly Yinlin Dong |
| author_facet | Hassan Abd Salman Al-Dujaly Yinlin Dong |
| author_sort | Hassan Abd Salman Al-Dujaly |
| collection | DOAJ |
| description | For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated and compared to show the features of high order schemes. Furthermore, there is a plan to study the stability and accuracy properties of the present schemes and apply them to standard systems of time dependent partial differential equations in CFD. |
| format | Article |
| id | doaj-art-03edbebc1da143519569e97c123efefa |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2020-09-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-03edbebc1da143519569e97c123efefa2025-08-20T03:58:10ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862020-09-01173(Suppl.)10.21123/bsj.2020.17.3(Suppl.).1041Matrix Form of Deriving High Order Schemes for the First DerivativeHassan Abd Salman Al-Dujaly0Yinlin Dong1Mustansiriyah UniversityUniversity of Central Arkansas, Arkansas, USAFor many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated and compared to show the features of high order schemes. Furthermore, there is a plan to study the stability and accuracy properties of the present schemes and apply them to standard systems of time dependent partial differential equations in CFD.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4329Compact Scheme, Dispersion, Dissipation, High Order, Wave Number |
| spellingShingle | Hassan Abd Salman Al-Dujaly Yinlin Dong Matrix Form of Deriving High Order Schemes for the First Derivative مجلة بغداد للعلوم Compact Scheme, Dispersion, Dissipation, High Order, Wave Number |
| title | Matrix Form of Deriving High Order Schemes for the First Derivative |
| title_full | Matrix Form of Deriving High Order Schemes for the First Derivative |
| title_fullStr | Matrix Form of Deriving High Order Schemes for the First Derivative |
| title_full_unstemmed | Matrix Form of Deriving High Order Schemes for the First Derivative |
| title_short | Matrix Form of Deriving High Order Schemes for the First Derivative |
| title_sort | matrix form of deriving high order schemes for the first derivative |
| topic | Compact Scheme, Dispersion, Dissipation, High Order, Wave Number |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4329 |
| work_keys_str_mv | AT hassanabdsalmanaldujaly matrixformofderivinghighorderschemesforthefirstderivative AT yinlindong matrixformofderivinghighorderschemesforthefirstderivative |