Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation
This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. T...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-06-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023216?viewType=HTML |
| _version_ | 1797691001972719616 |
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| author | Akeel A. AL-saedi Jalil Rashidinia |
| author_facet | Akeel A. AL-saedi Jalil Rashidinia |
| author_sort | Akeel A. AL-saedi |
| collection | DOAJ |
| description | This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the $L_2$ and $ {L_\infty } $ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method. |
| first_indexed | 2024-03-12T02:07:18Z |
| format | Article |
| id | doaj.art-81c8c7bcf1624557a8bd4ec241df8407 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-03-12T02:07:18Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-81c8c7bcf1624557a8bd4ec241df84072023-09-07T02:27:19ZengAIMS PressElectronic Research Archive2688-15942023-06-013174248426510.3934/era.2023216Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equationAkeel A. AL-saedi 0Jalil Rashidinia 1School of Mathematics and Computer Science, Iran University of Science & Technology, Tehran 16846-13114, IranSchool of Mathematics and Computer Science, Iran University of Science & Technology, Tehran 16846-13114, IranThis paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the $L_2$ and $ {L_\infty } $ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method.https://www.aimspress.com/article/doi/10.3934/era.2023216?viewType=HTMLtime-fractional burger's equationcaputo derivativeb-spline galerkin methoddifferent weight function |
| spellingShingle | Akeel A. AL-saedi Jalil Rashidinia Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation Electronic Research Archive time-fractional burger's equation caputo derivative b-spline galerkin method different weight function |
| title | Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation |
| title_full | Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation |
| title_fullStr | Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation |
| title_full_unstemmed | Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation |
| title_short | Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation |
| title_sort | application of the b spline galerkin approach for approximating the time fractional burger s equation |
| topic | time-fractional burger's equation caputo derivative b-spline galerkin method different weight function |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023216?viewType=HTML |
| work_keys_str_mv | AT akeelaalsaedi applicationofthebsplinegalerkinapproachforapproximatingthetimefractionalburgersequation AT jalilrashidinia applicationofthebsplinegalerkinapproachforapproximatingthetimefractionalburgersequation |