Abstract In this paper we first establish the existence, uniqueness and Hölder continuity of solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, singularities $\alpha \in (0, 1)$ for drift term $\beta 1/2)$ term. Subsequently, propose a $\theta $-Euler–Maruyama scheme Milstein solve numerically obtain strong rates convergence both schemes in $L^{p}$ norm any...

We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods for solving such systems. The main purpose of this paper is the derivation of global convergent and super-convergent properties of introduced methods on the graded meshes. We apply relevant methods to a ...

In this article, we consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. In the first part, we deal with two-dimensional integralalgebraic equations. Next, we analyze Volterra integral equations of the first kind with a degenerate matrix-kernel on the diagonal. Finally, the third part of the work is devoted to the analysis of degenerate integro...

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...