Abstract
Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations (NTFWEs) is considered in this paper. To this end, an alternating direction implicit (ADI) numerical scheme is derived. The scheme is established by combining the second-order convolution quadrature formula and Crank–Nicolson technique in time and a fourth-order difference approach in space. The convergence and unconditional stability of the proposed compact ADI scheme are strictly discussed after a concise solvability analysis. A numerical example is shown to demonstrate the theoretical analysis.
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