Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind

Collocation Solutions of a Weakly Singular Volterra Integral Equation

p(t, s) := s tμ , (1.2) where μ > 0, K(t, s) is a smooth function and g is a given function, can arise, e.g., in heat conduction problems with mixed boundary conditions ([2], [10]). The case when K(t, s) = 1 has been considered in several papers. The following lemma summarizes the analytical results for (1.1) in the case K(t, s) = 1. Lemma 1.1. (a) [12] Let μ > 1 in (1.2). If the function g bel...

Product integration for Volterra integral equations of the second kind with weakly singular kernels

We introduce a new numerical approach for solving Volterra integral equations of the second kind when the kernel contains a mild singularity. We give a convergence result. We also present numerical examples which show the performance and efficiency of our method.

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind

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 ...

Numerical method for non-linear fuzzy Volterra integral equations of the second kind