Li, Xuhao; Wong, Patricia J. Y. An efficient numerical treatment of fourth-order fractional diffusion-wave problems. (English) Zbl 1407.74099 Numer. Methods Partial Differ. Equations 34, No. 4, 1324-1347 (2018). Summary: 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. Cited in 11 Documents MSC: 74S20 Finite difference methods applied to problems in solid mechanics 76M20 Finite difference methods applied to problems in fluid mechanics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65D07 Numerical computation using splines 35R11 Fractional partial differential equations 76Q05 Hydro- and aero-acoustics 86A15 Seismology (including tsunami modeling), earthquakes 35Q35 PDEs in connection with fluid mechanics 35Q74 PDEs in connection with mechanics of deformable solids 74D10 Nonlinear constitutive equations for materials with memory 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:diffusion-wave equation; fractional differential equation; numerical solution; parametric quintic spline; stability and convergence PDFBibTeX XMLCite \textit{X. Li} and \textit{P. J. Y. Wong}, Numer. Methods Partial Differ. Equations 34, No. 4, 1324--1347 (2018; Zbl 1407.74099) Full Text: DOI