The study analyzed the influence of artificially introduced local inhomogeneities (defects) on the dynamics of the cellular-automaton solution of the scalar wave equation. We used a cellular-automaton scheme, which is taken from the Crank-Nicolson mesh scheme. To estimate the relationship between the perturbed and unperturbed solutions, we introduced an integral characteristic of the “energy” of the cellular automaton field. The computational experiment showed that, despite the oscillation phase drift, the average “energy” and its deviation are conserved, and the solution is not destroyed. Findings of the research show that the “energy” deviation is proportional to the total distance of the defects to the symmetry center.
Matyushkin I.V., Zapletina M.A. Influence of point defects in the structure of a cellular-automaton calculator on the solution of a 2D scalar wave equation.Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 3–19.