A novel iteration scheme, using boundary integral equations, is developed for error estimation in the boundary element method. The iteration scheme consists of using the boundary integral equation for solving the boundary value problem and iterating this solution with the hypersingular boundary integral equation to obtain a new solution. The hypersingular residual r is consistently defined as t...

This paper presents an extension of McKean’s (1965) incomplete Fourier transform method to solve the two-factor partial differential equation for the price and early exercise surface of an American call option, in the case where the volatility of the underlying evolves randomly. The Heston (1993) square-root process is used for the volatility dynamics. The price is given by an integral equation...

The numerical treatment of boundary integral equations in the form of boundary element methods has became very popular and powerful tool for engineering computations of boundary value problems, in addition to finite difference and finite element methods. Here, we present some of the most important analytical and numerical aspects of the boundary integral equation. The concept of the principle s...

A hierarchical multilevel preconditioner is constructed for an efficient solution of a first kind boundary integral equation with the single layer potential operator discretized by a boundary element method. This technique is based on a hierarchical clustering of all boundary elements as used in fast boundary element methods. This hierarchy is applied to define a sequence of nested boundary ele...

The paper presents the effectiveness of the parametric integral equation system (PIES) in solving 3D boundary problems defined by Navier-Lame equations on the example of the polygonal boundary and in comparison with the boundary element method (BEM). Analysis was performed using the commercial software “BEASY” which bases on the BEM method, whilst in the case of PIES using an authors software. ...

We consider the solution of high-frequency scattering problems in two dimensions, modelled by an integral equation on the boundary of the scattering object. We devise a numerical method to obtain solutions on only parts of the boundary with little computational effort. The method incorporates asymptotic properties of the solution and can therefore attain particularly good results for high frequ...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...