An approximate solution of a class of nonlinear partial integro-differential equations by the method of expanding the state space

In this paper, to simulate transient regimes in evolutionary systems described by non-linear partial integro-differential equations of Volterra type (PIDEs), we use the method based on approximation of kernels of equations, expanding the state space that allows us to construct a chain of PIDEs without integral terms. The results of calculations performed in the environment of the it Mathematica mathematical package are demonstrated for the case of a kernal that is specific for deterministic viscoelastic systems.