FredholmVolterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions
Abstract
In this paper, the existence and uniqueness of solution of the FredholmVolterra integral equation (FVIE), with a generalized singular kernel, are discussed and proved in the spaceL_{2}(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.
 Publication:

Icms International Conference on Mathematical Science
 Pub Date:
 November 2010
 DOI:
 10.1063/1.3525135
 Bibcode:
 2010AIPC.1309...33E
 Keywords:

 integral equations;
 numerical analysis;
 linear algebra;
 Galerkin method;
 02.30.Rz;
 02.60.Cb;
 02.10.Ud;
 02.70.Dh;
 Integral equations;
 Numerical simulation;
 solution of equations;
 Linear algebra;
 Finiteelement and Galerkin methods