Numerical algorithm for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term
Provides a numerical method for a specific class of fractional PDEs, incremental for computational mathematics.
The paper develops an ADI difference scheme for a 2D time-fractional wave equation with a nonlinear source term, proving unconditional stability and convergence. Numerical experiments confirm the algorithm's effectiveness.
In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is discussed, and the unconditional stability and convergence order of the numerical scheme are analysed. Finally, numerical experiments are carried out to verify the effectiveness and accuracy of the algorithm.