On a weakly singular integral equation and its application

On a weakly singular integral equation and its application

A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier. c © 2008 Published by Elsevier Ltd

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

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

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...