A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS

Melis Zorsahin Gorgulu; İdris Dag; Sumeyye Dogan; Dursun Irk

doi:10.18038/aubtda.336116

EN

A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS

Abstract

In this paper, numerical solution of the advection-diffusion equation is obtained by using extended cubic B-spline functions. For space discretization, the extended cubic B-spline Galerkin method is used to integrate the advection-diffusion equation and for time discretization, the Crank-Nicolson method is employed to obtain the fully integrated advection-diffusion equation. The maximum error norm has been used to show the accuracy of the method. Robustness of the suggested method is shown by studying some classical test problems and comparing the results with some earlier ones.

Keywords

Extended cubic B-spline,Galerkin finite element method,advection-diffusion equation

References

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Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Melis Zorsahin Gorgulu
Eskisehir Osmangazi University, Central Research Laboratory Application and Research Center (ARUM), Odunpazari, Eskisehir, Turkey
Türkiye

İdris Dag
Eskisehir Osmangazi University, Central Research Laboratory Application and Research Center (ARUM), Odunpazari, Eskisehir, Turkey
Türkiye

Sumeyye Dogan This is me
Eskisehir Osmangazi University, Central Research Laboratory Application and Research Center (ARUM), Odunpazari, Eskisehir, Turkey
Türkiye

Dursun Irk
Eskisehir Osmangazi University, Central Research Laboratory Application and Research Center (ARUM), Odunpazari, Eskisehir, Turkey
Türkiye

Publication Date

March 31, 2018

Submission Date

August 25, 2017

Acceptance Date

March 7, 2018

Published in Issue

Year 2018 Volume: 19 Number: 2

DOI

https://doi.org/10.18038/aubtda.336116

IZ

https://izlik.org/JA36KX89MN

APA

Zorsahin Gorgulu, M., Dag, İ., Dogan, S., & Irk, D. (2018). A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 19(2), 347-355. https://doi.org/10.18038/aubtda.336116

AMA

1.Zorsahin Gorgulu M, Dag İ, Dogan S, Irk D. A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS. AUJST-A. 2018;19(2):347-355. doi:10.18038/aubtda.336116

Chicago

Zorsahin Gorgulu, Melis, İdris Dag, Sumeyye Dogan, and Dursun Irk. 2018. “A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19 (2): 347-55. https://doi.org/10.18038/aubtda.336116.

EndNote

Zorsahin Gorgulu M, Dag İ, Dogan S, Irk D (June 1, 2018) A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19 2 347–355.

IEEE

[1]M. Zorsahin Gorgulu, İ. Dag, S. Dogan, and D. Irk, “A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS”, AUJST-A, vol. 19, no. 2, pp. 347–355, June 2018, doi: 10.18038/aubtda.336116.

ISNAD

Zorsahin Gorgulu, Melis - Dag, İdris - Dogan, Sumeyye - Irk, Dursun. “A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19/2 (June 1, 2018): 347-355. https://doi.org/10.18038/aubtda.336116.

JAMA

1.Zorsahin Gorgulu M, Dag İ, Dogan S, Irk D. A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS. AUJST-A. 2018;19:347–355.

MLA

Zorsahin Gorgulu, Melis, et al. “A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 19, no. 2, June 2018, pp. 347-55, doi:10.18038/aubtda.336116.

Vancouver

1.Melis Zorsahin Gorgulu, İdris Dag, Sumeyye Dogan, Dursun Irk. A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS. AUJST-A. 2018 Jun. 1;19(2):347-55. doi:10.18038/aubtda.336116

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