Two alternating direction implicit difference schemes for solving the two-dimensional time distributed-order wave equations
The authors study two alternating direction implicit difference schemes for solving the two-dimensional time distributed-order wave equations. They first provide numerical quadrature formulae, a fractional numerical differentiation formula and some useful notations. Derivation of alternating direction implicit (ADI) difference scheme in space and distributed order with unconditional stability and convergence analysis is given. A fourth-order difference scheme and its stability and convergence using the discrete energy method are provided. Numerical experiments are given to illustrate the efficiency and numerical convergence orders of the proposed algorithms.
alternating direction implicit difference scheme
scientific article; zbMATH DE number 6759213
scientific article