Numerical solution of integro-differential equations of the theory of viscoelasticity with kernels of exponential and Rabotnov types

In differential equations describing the behavior of continuous media with creep, in accordance with Volterra’s linear theory, applicable to a wide range of materials with amorphous and heterogeneous structure, integral type operators are present. In these equations, the kernel of the integral operator is represented as a sum of exponentials, or as a weakly singular kernel (the Rabotnov function). Obtaining an analytical solution for the equations in question is problematic in some cases, hence the need to develop a numerical method and algorithm for solving such equations, taking into account the memory of the medium in question. To solve these equations, the paper uses the grid-characteristic method and the coordinate splitting method (for multidimensional problems). The approximation and stability of the proposed method are numerically investigated.