High-order difference scheme for the solution of linear time fractional Klein-Gordon equations (Q2875714)

The authors consider the equations named in the title, including a fractional time derivative taken in the sense of Caputo, of order \(1<\alpha\leq 2\). Their equation also contains a second-order derivative in the space variable and may contain a partial derivative of first order and the function itself. Following mainly work of Sun and coworkers [\textit{R. Du} et al., Appl. Math. Modelling 34, No. 10, 2998--3007 (2010; Zbl 1201.65154)], and of \textit{S. Chen} et al. [ibid. 33, No. 1, 256--273 (2009; Zbl 1167.65419)], they construct a compact difference scheme of order 4 in space and \(\tau^{3-\alpha}\) in time and prove its solvability (the matrix involved is shown to be strictly diagonally dominant and multiplies the numerical solution on all time levels), unconditional stability and convergence of the order indicated. They also provide numerical results of 3 test problems, corresponding to the theoretical results.