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## Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting

#### Yusuf UÇAR [1] , Murat YAĞMURLU [2] , İhsan ÇELİKKAYA [3]

The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been splitted according to the time term and then has been solved by finite element collocation method using cubic B-spline bases. By splitting the equation U_{t}+UU_{x}=vU_{xx} two simpler sub problems U_{t}+UU_{x}=0 and  U_{t}-vU_{xx}=0 have been obtained. A discretization process has been performed for each of these sub-problems and the stability analyzes have been carried out by Fourier (von Neumann) series method. Then, both sub-problems have been solved using the Strang splitting technique to obtain numerical results. To see the effectiveness of the present method, which is a combination of finite element method and Strang splitting technique, we have calculated the frequently used error norms ‖e‖₁, L₂ and L_{∞} in the literature and have made a comparison between exact and a numerical solution.
Strang Splitting, Burgers Equation, Collocation method, Finite Element method, Cubic B-Spline Basis
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Primary Language en Engineering Articles Orcid: 0000-0003-1469-5002Author: Yusuf UÇAR Institution: INONU UNIVERSITYCountry: Turkey Orcid: 0000-0003-1593-0254Author: Murat YAĞMURLU (Primary Author)Institution: INONU UNIVERSITYCountry: Turkey Orcid: 0000-0002-8684-5922Author: İhsan ÇELİKKAYA Institution: BATMAN VOCATIONAL SCHOOLCountry: Turkey Publication Date : March 20, 2020
 Bibtex @research article { mathenot598635, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {29 - 45}, doi = {10.36753/mathenot.598635}, title = {Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting}, key = {cite}, author = {Uçar, Yusuf and Yağmurlu, Murat and Çeli̇kkaya, İhsan} } APA Uçar, Y , Yağmurlu, M , Çeli̇kkaya, İ . (2020). Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting . Mathematical Sciences and Applications E-Notes , 8 (1) , 29-45 . DOI: 10.36753/mathenot.598635 MLA Uçar, Y , Yağmurlu, M , Çeli̇kkaya, İ . "Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 29-45 Chicago Uçar, Y , Yağmurlu, M , Çeli̇kkaya, İ . "Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting". Mathematical Sciences and Applications E-Notes 8 (2020 ): 29-45 RIS TY - JOUR T1 - Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting AU - Yusuf Uçar , Murat Yağmurlu , İhsan Çeli̇kkaya Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.598635 DO - 10.36753/mathenot.598635 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 29 EP - 45 VL - 8 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.598635 UR - https://doi.org/10.36753/mathenot.598635 Y2 - 2020 ER - EndNote %0 Mathematical Sciences and Applications E-Notes Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting %A Yusuf Uçar , Murat Yağmurlu , İhsan Çeli̇kkaya %T Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 1 %R doi: 10.36753/mathenot.598635 %U 10.36753/mathenot.598635 ISNAD Uçar, Yusuf , Yağmurlu, Murat , Çeli̇kkaya, İhsan . "Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting". Mathematical Sciences and Applications E-Notes 8 / 1 (March 2020): 29-45 . https://doi.org/10.36753/mathenot.598635 AMA Uçar Y , Yağmurlu M , Çeli̇kkaya İ . Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting. Math. Sci. Appl. E-Notes. 2020; 8(1): 29-45. Vancouver Uçar Y , Yağmurlu M , Çeli̇kkaya İ . Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 29-45. IEEE Y. Uçar , M. Yağmurlu and İ. Çeli̇kkaya , "Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting", Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, pp. 29-45, Mar. 2020, doi:10.36753/mathenot.598635

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