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An efficient numerical treatment of fourth‐order fractional diffusion‐wave problems
Author(s) -
Li Xuhao,
Wong Patricia J. Y.
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22260
Subject(s) - mathematics , convergence (economics) , parametric statistics , stability (learning theory) , quintic function , scheme (mathematics) , fractional calculus , numerical stability , numerical analysis , mathematical analysis , computer science , statistics , physics , nonlinear system , quantum mechanics , machine learning , economics , economic growth
In this paper, we consider the numerical treatment of a fourth‐order fractional diffusion‐wave problem. Our proposed method includes the use of parametric quintic spline in the spatial dimension and the weighted shifted Grünwald‐Letnikov approximation of fractional integral. The solvability, stability, and convergence of the numerical scheme are rigorously proved. It is shown that the theoretical convergence order improves those of earlier work. Simulation is further carried out to demonstrate the numerical efficiency of the proposed scheme and to compare with other methods.