Numerical Solution of Integro-Differential Equations of Viscoelasticity with Kernels of Exponential and Rabotnov Types

Differential equations describing the behavior of continuous media with creep involve integral type operators, in accordance with Volterra’s linear theory, which is applicable to a wide range of materials with amorphous and heterogeneous structures. In these equations, the kernel of the integral operator is represented as a sum of exponentials or as a weakly singular kernel (Rabotnov function). Obtaining an analytical solution for the equations in question is problematic in some cases, so it is necessary to develop a numerical method and algorithm, taking into account the memory of the considered medium. In this paper, the equations are solved using the grid-characteristic method and dimensional splitting (for multidimensional problems). The approximation and stability of the proposed method are numerically investigated.