On a Certain Finite-Difference Scheme for a Hereditary Oscillatory Equation

In this paper, we proposed an explicit finite-difference scheme for numerical simulation of the Cauchy problem for a nonlinear integro-differential equation that describes an oscillatory process with friction and memory (heredity) and the corresponding local initial conditions. Approximation, stability, and convergence of the finite-difference scheme are examined. Results of computer experiments that implement the numerical scheme proposed confirm theoretical estimates.