The paper «On a Finite-Difference Scheme for an Hereditary Oscillatory Equation» has been published

   The paper proposes an explicit finite-difference scheme for numerical simulation of the Cauchy problem with an integro-differential nonlinear equation that describes an oscillatory process with friction and memory (hereditarity), and with the corresponding local initial conditions. The problems of approximation, stability, and convergence of the proposed finite-difference scheme are investigated. The results of computer experiments that implement the proposed numerical scheme, confirming the theoretical estimates obtained in theorems, are given.

   Parovik R. On a Finite-Difference Scheme for an Hereditary Oscillatory Equation. Journal of Mathematical Sciences. 2021. V. 253. No. 4. pp. 547-557. DOI:10.1007/s10958-021-05252-2