Matrix Form of Deriving High Order Schemes for the First Derivative

Main Article Content

Hassan Abd Salman Al-Dujaly
https://orcid.org/0000-0001-9771-0129
Yinlin Dong
http://orcid.org/0000-0003-4030-3383

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.   

Article Details

How to Cite
1.
Matrix Form of Deriving High Order Schemes for the First Derivative. Baghdad Sci.J [Internet]. 2020 Sep. 8 [cited 2024 Mar. 28];17(3(Suppl.):1041. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4329
Section
article
Author Biography

Hassan Abd Salman Al-Dujaly, Mustansiriyah University

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, we 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.    

How to Cite

1.
Matrix Form of Deriving High Order Schemes for the First Derivative. Baghdad Sci.J [Internet]. 2020 Sep. 8 [cited 2024 Mar. 28];17(3(Suppl.):1041. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4329

Similar Articles

You may also start an advanced similarity search for this article.