A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

• Main Authors: Nauman Khalid, Muhammad Abbas, Muhammad Kashif Iqbal, Dumitru Baleanu
• Format: Article
• Language: English
• Published: SpringerOpen 2019-09-01
• Series: Advances in Difference Equations
• Subjects: Time-fractional diffusion wave equation; Finite difference formulation; Caputo’s time-fractional derivative; Modified extended B-spline functions; Modified B-spline collocation method
• Online Access: http://link.springer.com/article/10.1186/s13662-019-2318-7

Abstract In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.