Application of trigonometric B-spline functions for solving Caputo time fractional gas dynamics equation

Rabia Noureen; Muhammad Nawaz Naeem; Dumitru Baleanu; Pshtiwan Othman Mohammed; Musawa Yahya Almusawa; Rabia Noureen; Muhammad Nawaz Naeem; Dumitru Baleanu; Pshtiwan Othman Mohammed; Musawa Yahya Almusawa

doi:10.3934/math.20231293

AIMS Mathematics

2023, Volume 8, Issue 11: 25343-25370. doi: 10.3934/math.20231293

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Application of trigonometric B-spline functions for solving Caputo time fractional gas dynamics equation

1.
Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
3.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
6.
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia

Received: 12 May 2023 Revised: 24 July 2023 Accepted: 20 August 2023 Published: 01 September 2023
MSC : 33B10, 26A51, 26A48, 39B62, 39A12

In this study, we present a numerical method that utilizes trigonometric cubic B-spline functions to solve the time fractional gas dynamics equation, which is a key component in the study of physical phenomena such as explosions, combustion, detonation and condensation in a moving flow. The Caputo formula is used to define the fractional time derivative, which generalizes the framework for both singular and non-singular kernels. To discretize the unknown function and its derivatives in the spatial direction, we employ trigonometric cubic B-spline functions, while the usual finite difference formulation is used to approximate the Caputo time fractional derivative. A stability analysis of the scheme is provided to ensure that errors do not propagate over time, and a convergence analysis is conducted to measure the accuracy of the solution. To demonstrate the effectiveness of the proposed methodology, we solve various relevant examples and present graphical and tabular results to evaluate the outcomes of the strategy.
- time fractional gas dynamics equation,
- trigonometric cubic B-spline functions,
- finite difference formulation,
- collocation method,
- stability,
- convergence analysis
Citation: Rabia Noureen, Muhammad Nawaz Naeem, Dumitru Baleanu, Pshtiwan Othman Mohammed, Musawa Yahya Almusawa. Application of trigonometric B-spline functions for solving Caputo time fractional gas dynamics equation[J]. AIMS Mathematics, 2023, 8(11): 25343-25370. doi: 10.3934/math.20231293

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Abstract

In this study, we present a numerical method that utilizes trigonometric cubic B-spline functions to solve the time fractional gas dynamics equation, which is a key component in the study of physical phenomena such as explosions, combustion, detonation and condensation in a moving flow. The Caputo formula is used to define the fractional time derivative, which generalizes the framework for both singular and non-singular kernels. To discretize the unknown function and its derivatives in the spatial direction, we employ trigonometric cubic B-spline functions, while the usual finite difference formulation is used to approximate the Caputo time fractional derivative. A stability analysis of the scheme is provided to ensure that errors do not propagate over time, and a convergence analysis is conducted to measure the accuracy of the solution. To demonstrate the effectiveness of the proposed methodology, we solve various relevant examples and present graphical and tabular results to evaluate the outcomes of the strategy.

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