Efficient numerical algorithm with the second-order time accuracy for a two-dimensional nonlinear fourth-order fractional wave equation

In this article, we construct an efficient numerical algorithm with the second-order time accuracy for a two-dimensional nonlinear fourth-order fractional wave equation. We introduce an auxiliary variable to transform the fractional fourth-order wave problem into a low order coupled system, and then integrate the resulting equations by using Riemann-Liouville fractional integral. For the obtained fractional integral system, we use the Crank-Nicolson scheme in time with the weighted and shifted Grunwald integral (WSGI) approximation and the finite element method in space to arrive at the fully discrete coupled system. We show the detailed numerical algorithms and carry out numerical tests by taking two two-dimensional examples on rectangular and circular space domains to verify the effectiveness and convergence efficiency for our algorithm.(C) 2022 The Author(s). Published by Elsevier B.V.& nbsp;