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- Title
Matrix Form of Deriving High Order Schemes for the First Derivative.
- Authors
Salman Al-Dujaly, Hassan Abd; Yinlin Dong
- Abstract
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.
- Subjects
COMPUTATIONAL fluid dynamics; PARTIAL differential equations; COMPUTATIONAL physics; UNITS of time
- Publication
Baghdad Science Journal, 2020, Vol 17, p1041
- ISSN
2078-8665
- Publication type
Article
- DOI
10.21123/bsj.2020.17.3(Suppl.).1041