p-Sparse BEM for weakly singular integral equation with random data

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...

On the Volterra Integral Equation with Weakly Singular Kernel

Extrapolation Methods for a Nonlinear Weakly Singular Volterra Integral Equation

In this work we consider a nonlinear Volterra integral equation with weakly singular kernel. An asymptotic error expansion for the explicit Euler’s method is obtained and this allows the use of certain extrapolation procedures. The performance of the extrapolation method is illustrated by several numerical examples.

Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement

We consider the adaptive lowest-order boundary element method (ABEM) based on isotropic mesh-refinement for the weakly-singular integral equation for the 3D Laplacian. The proposed scheme resolves both, possible singularities of the solution as well as of the given data. The implementation thus only deals with discrete integral operators, i.e. matrices. We prove that the usual adaptive mesh-ref...

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...