Two Alternating Direction Implicit Difference Schemes for Solving the Two-Dimensional Time Distributed-Order Wave Equations

Two alternating direction implicit difference schemes are established for solving a class of two-dimensional time distributed-order wave equations. The schemes are proved to be unconditionally stable and convergent in the maximum norm with the convergence orders $$O(\tau ^2+h_1^2+h_2^2+\Delta \gamma ^2)$$O(τ2+h12+h22+Δγ2) and $$O(\tau ^2+h_1^4+h_2^4+\Delta \gamma ^4),$$O(τ2+h14+h24+Δγ4), respectively, where $$\tau , h_i\; (i=1,2)$$τ,hi(i=1,2) and $$\Delta \gamma $$Δγ are the step sizes in time, space and distributed order. Also, several numerical experiments are carried out to validate the theoretical results.

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