An effective approach based on Hybrid B-spline to solve Riesz space fractional partial differential equations

M. S. Hashmi; Rabia Shikrani; Farwa Nawaz; Ghulam Mustafa; Kottakkaran Sooppy Nisar; Velusamy Vijayakumar; M. S. Hashmi; Rabia Shikrani; Farwa Nawaz; Ghulam Mustafa; Kottakkaran Sooppy Nisar; Velusamy Vijayakumar

doi:10.3934/math.2022576

AIMS Mathematics

2022, Volume 7, Issue 6: 10344-10363. doi: 10.3934/math.2022576

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An effective approach based on Hybrid B-spline to solve Riesz space fractional partial differential equations

1.
Department of Mathematics, The Government Sadiq College Women University, Bahawalpur, Pakistan
2.
Department of Mathematics, The Islamia University of Bahawalpur, Pakistan
3.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia
4.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamilnadu, India

Received: 05 November 2021 Revised: 05 November 2021 Accepted: 20 February 2022 Published: 25 March 2022
MSC : 35R11, 41A15

B-spline is extensively used for the solution of many physical models appearing in the fields of plasma physics, fluid mechanics, atmosphere-ocean dynamics and many other disciplines. In this article, Riesz space fractional PDEs (RSF-PDEs) in two forms are solved by using hybrid B-spline collocation method (HBCM). In the given methodology, RSF-PDEs are discretized into the system of algebraic linear equations by using hybrid B-spline basis function. The resultant system is solved by a numerical technique. The Von Neumann stability analysis method is used for analyzing the stability of proposed method. Numerical experiments are conducted to illustrate the accuracy of proposed method, by representing the results graphically and numerically for different values of fractional parameters.
- collocation method,
- fractional PDE,
- B-spline functions,
- numerical method,
- Von Neumann stability analysis
Citation: M. S. Hashmi, Rabia Shikrani, Farwa Nawaz, Ghulam Mustafa, Kottakkaran Sooppy Nisar, Velusamy Vijayakumar. An effective approach based on Hybrid B-spline to solve Riesz space fractional partial differential equations[J]. AIMS Mathematics, 2022, 7(6): 10344-10363. doi: 10.3934/math.2022576

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Abstract

B-spline is extensively used for the solution of many physical models appearing in the fields of plasma physics, fluid mechanics, atmosphere-ocean dynamics and many other disciplines. In this article, Riesz space fractional PDEs (RSF-PDEs) in two forms are solved by using hybrid B-spline collocation method (HBCM). In the given methodology, RSF-PDEs are discretized into the system of algebraic linear equations by using hybrid B-spline basis function. The resultant system is solved by a numerical technique. The Von Neumann stability analysis method is used for analyzing the stability of proposed method. Numerical experiments are conducted to illustrate the accuracy of proposed method, by representing the results graphically and numerically for different values of fractional parameters.

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