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    On numerical solution of the time-fractional diffusion-wave equation with the fictitious time integration method
    (SPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, 2019) Hashemi, Mir Sajjad; İnç, Mustafa; Parto-Haghighi, Mohammad; Bayram, Mustafa
    In this work we offer a robust numerical algorithm based on the Lie group to solve the timefractional diffusion-wave (TFDW) equation. Firstly, we use a fictitious time variable ? to convert the related variable u(x, t) into a new space with one extra dimension. Then by using a composition of the group preserving scheme (GPS) and a semi-discretization of new variable, we approximate the solutions of the problem. Finally, various numerical experiments are performed to illustrate the power and accuracy of the given method.