Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation

Akeel A. AL-saedi; Jalil Rashidinia; Akeel A. AL-saedi; Jalil Rashidinia

doi:10.3934/era.2023216

Electronic Research Archive

2023, Volume 31, Issue 7: 4248-4265. doi: 10.3934/era.2023216

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Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation

Akeel A. AL-saedi ,
Jalil Rashidinia ^,

School of Mathematics and Computer Science, Iran University of Science & Technology, Tehran 16846-13114, Iran

Received: 23 March 2023 Revised: 02 May 2023 Accepted: 06 May 2023 Published: 01 June 2023

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.
- time-fractional Burger's equation,
- Caputo derivative,
- B-spline Galerkin method,
- different weight function
Citation: Akeel A. AL-saedi, Jalil Rashidinia. Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation[J]. Electronic Research Archive, 2023, 31(7): 4248-4265. doi: 10.3934/era.2023216

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Abstract

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.

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