‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

We consider mixed boundary value problems in Physical Geodesy and study possibilities in order to transform them into a system of integral equations over the boundary of the domain. The system of integral equations can be solved numerically, by, e.g. boundary element methods, provided that (a) the mixed boundary value problem is uniquely solvable, (b) the system of integral equations is equival...

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by ...

The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crac...

Acoustic scattering by three-dimensional obstacles is considered, using boundary integral equations, null-field equations and the T-matrix. Connections between these techniques are explored. It is shown that solving a boundary integral equation by a particular Petrov–Galerkin method leads to the same algebraic system as obtained from the null-field equations. It is also emphasised that the T-ma...

The optical eld in a weakly guiding homogeneous waveguide satis es scalar Helmholtz equations in both the core and cladding, and transmission conditions on the boundary. The transverse wavenumbers of the two scalar Helmholtz equations for the core and cladding are di erent and both of them depend on the propagation constants in the longitudinal direction of the waveguide. Two di erent systems o...

Fredholm integral equations arise naturally in the context of ordinary and partial differential equations: Two-point boundary value problems can be reformulated as Fredholm integral equations, whose kernels are continuous but have finite jump discontinuities in their derivatives. Two-dimensional elliptic boundary problems can be reformulated as Fredholm integral equations with kernels that have...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...