We consider solving integral equations on a piecewise smooth surface S in R 3 with a smooth kernel function, using piecewise polynomial collocation interpolation of the surface. The theoretical analysis includes the eeects of the numerical integration of the collocation coeecients and the use of the approximating surface. The resulting order of convergence is higher than had previously been exp...

A numerical method for solving linear integral equations of the second kind is formulated. Based on a special representation of vector forms of triangular functions and the related operational matrix of integration, the integral equation reduces to a linear system of algebraic equations. Generation of this system needs no integration, so all calculations can easily be implemented. Numerical res...

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be...

This guide describes a collection of programs for creating and re ning triangulations on surfaces and solving integral equations using collocation methods over these tri angulations The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are de ned on piecewise smooth surfaces in R For a general survey of the numerical...

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...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...