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\begin{document}

\title{Two linearized finite difference schemes for time fractional nonlinear
diffusion-wave equations with fourth order derivative}



\author[1]{Emadidin Elmahdi}%
\author[1]{JianFei Huang}%
\affil[1]{Yangzhou University}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\begin{abstract}
In this paper, we present a finite difference and a compact finite
difference schemes for the time fractional nonlinear diffusion-wave
equations (TFNDWEs) with the space fourth order derivative. To reduce
the smoothness requirement in time, the considered TFNDWEs are
equivalently transformed into their partial integro-differential forms
with the classical first order integrals and the Caputo derivative. The
finite difference scheme is constructed by using Crank-Nicolson method
combined with the midpoint formula, the weighted and shifted
Gr\$\textbackslash{}ddot\{u\}\$nwald difference formula and the second
order convolution quadrature formula to deal with the temporal
discretizations. Meanwhile, the classical central difference formula and
fourth order Stephenson scheme are used in spacial direction. Then, the
compact finite difference scheme is developed by using the fourth order
compact difference formula for the spatial direction. The stability and
convergence of the proposed schemes are strictly proved by using the
discrete energy method. Finally, some numerical experiments are
presented to support our theoretical results.%
\end{abstract}%



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