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Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms. (English) Zbl 1459.65198

Adv. Difference Equ. 2019, Paper No. 378, 19 p. (2019).
Summary: 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.

Cited in 11 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

time-fractional diffusion wave equation; finite difference formulation; Caputo’s time-fractional derivative; modified extended B-spline functions; modified B-spline collocation method
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\textit{N. Khalid} et al., Adv. Difference Equ. 2019, Paper No. 378, 19 p. (2019; Zbl 1459.65198)
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References:

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