High-order rotated grid point iterative method for solving 2D time fractional telegraph equation and its convergence analysis

In this paper, the compact finite difference (CFD) and rotated four-point compact explicit decoupled group (CEDG) methods are proposed to solve the two-dimensional time-fractional telegraph equation. The CEDG method is derived from a rotated of CFD approximation formula combine with the arranging of the grid points in the form of a group. This method shows superior performance in the term of CPU timings and iteration compared to the CFD method on the standard grid but with the same order of accuracy. We have proved the stability and convergence of the proposed schemes using the Fourier analysis. The convergence order of the proposed methods is $$O\left( \tau +h_{x}^{4}+h_{y}^{4}\right) $$ . Some numerical experiments are performed to demonstrate the effectiveness of the proposed methods.