Some integral identities for the fttndamental solutions of potential and elastostatic problems are established in this paper. With these identities it is shown that the conventional boundary integral equation (BIE), which is generally expressed in terms of singularintegrals in the sense of the Cauchy principal value (CPV), and the derivative BIE, which is similarly expressed in terms of hypersi...

This article investigates an equation with a rapidly oscillating inhomogeneity and decreasing kernel of integral operator Fredholm type. Earlier, differential problems this type were studied in which the term was either absent or had form Volterra-type integral. The presence its significantly affect development algorithm for asymptotic solutions, implementation it is necessary to take into acco...

The subject of this paper is the formulation of boundary integral equations for firstand second-order shape sensitivities of boundary elastic fields in three-dimensional bodies. Here the direct differentiation approach is considered. It relies on the repeated application of the material derivative concept to the governing regularized (i.e. weakly singular) displacement boundary integral equatio...

This work is concerned with the construction and analysis of high order product integration methods for a class of Volterra integral equations with logarithmic singular kernel. Sufficient conditions for the methods to be convergent are derived and it is shown that optimal convergence orders are attained if the exact solution is sufficiently smooth. The case of non-smooth solutions is dealt with...

Abstract: In this article we have elaborated the numerical schemes of reduction methods for approximate solution of system of singular integro-differential equations when the kernel has a weak singularity. The equations are defined on the arbitrary smooth closed contour of complex plane. We suggest the numerical schemes of the reduction method over the system of Faber-Laurent polynomials for th...

Volterra subdiffusion problems with weakly singular kernel describe the dynamics of processes well. The graded L1 scheme is often chosen to discretize such since it can handle singularity solution near $$t = 0$$ . In this paper, we propose a modification. We first split time interval [0, T] into $$[0, T_0]$$ and $$[T_0, T]$$ , where $$T_0$$ ( $$0< T_0 < T$$ ) reasonably small. Then, applied in ...

The effect of non-stationary external forces on the vibration pipelines made composite materials is investigated in paper. A mathematical model pipeline developed, considering viscosity properties structure and base material, axial forces, internal pressure, resistance disturbances. viscoelastic conveying fluid under vibrations constructed based Boltzmann-Volterra integral model. to study a Eul...